title: Reservation in India

text: The Women's Reservation Bill was passed by the Rajya Sabha on 9 March 2010 by a majority vote of 186 members in favor and 1 against. As of March 2013, the Lok Sabha has not voted on the bill. Critics say gender cannot be held as a basis for reservation alone other factors should also be considered e.g. economic, social conditions of woman candidates especially when applying reservation for educated women. The criticism points that the policy benefits women that have access to political capital through family circles and are faced with the burden of a huge learning curve. Again, women are divided among caste and class lines with this dichotomy playing an important role in deciding how the presence of women in the lowest tier of governance impact the problems faced by the women of the constituency


title: Reservation in India

text: In Gujarat and Andhra Pradesh, 32% of posts are reserved for females in all government departments and services, such as police, health, education and general administration. From 2015 onwards Kerala has implemented a 55% reservation for all posts of its local self governing bodies.


title: Reservation in India

text: On 21 July 2021, Karnataka became the first state in the country to provide one percent reservation for the transgender community in all government services. The government submitted a report to the High Court in this regard, informing that a notification had already been issued after amending the Karnataka Civil Service. The job could be given to males or females, from the same category, in case of the non-availability of transgender candidates.


title: Reservation in India

text: The Tamil Nadu government has allotted 3.5% of seats each to Muslims and Christians, thereby altering the OBC reservation to 23% from 30% (since it excludes persons belonging to Other Backward Castes who are either Muslims or Christians).


title: Reservation in India

text: The Government of Andhra Pradesh introduced a law enabling 4 percent reservations for Muslims in 2004. This law was upheld by the Supreme Court in an interim order in 2010 but it constituted a Constitution bench to look further into the issue. The referral was to examine the constitutional validity of quotas based on religion. Kerala Public Service Commission has a quota of 12% for Muslims. Religious minority (Muslim or Christian) educational institutes also have 50% reservation for Muslim or Christian religions. The Central government has listed a number of Muslim communities as backward Muslims, making them eligible for reservation.


title: Reservation in India

text: The Union Government on 22 December 2011 announced the establishment of a sub-quota of 4.5% for religious minorities within the existing 27% reservation for Other Backward Classes. The reasoning given was that Muslim communities that have been granted OBC status are unable to compete with Hindu OBC communities. It was alleged that the decision was announced as the Election Commission announced Assembly elections in five states on 24 December 2011. The government would not have been able to announce this due to the model code of conduct. On 12 January 2012, the Election Commission stayed implementation of this decision for violation of the model code of conduct. Later, Justice Sachar, head of the Sachar Committee that was commissioned to prepare a report on the latest social, economic and educational condition of the Muslim community of India, criticised the government decision, saying "Such promises will not help the backward section of minorities. It is like befooling them. These people are making tall claims just to win elections". He suggested that instead of promising to give reservations, the government should focus on basic issues of improving administration and governance.


title: Reservation in India

text: On 28 May 2012, the Andhra Pradesh High Court quashed the sub-quota. The court said that the sub-quota has been carved out only on religious lines and not on any other intelligible basis. The court criticized the decision: "In fact, we must express our anguish at the rather casual manner in which the entire issue has been taken up by the central government.".


title: Reservation in India

text: Mandal commission protests of 1990 were against reservation in government jobs based on caste in India.


title: Reservation in India

text: The 2006 Indian anti-reservation protests were a series of protests that took place in India in 2006 in opposition to the decision of the Union Government of India, led by the Indian National Congress-headed multiparty coalition United Progressive Alliance, to implement reservations for the Other Backward Classes (OBCs) in central and private institutes of higher education. This move led to massive protests, particularly from students and doctors belonging to the forward castes, who claimed that the government's proposal was discriminatory, discarded meritocracy and was driven by "vote-bank politics".


title: Reservation in India

text: In 2008 and 2010, the Gujjar community in Rajasthan demanded reclassification from OBC to ST (Scheduled Tribes) for increased reservation benefits. They began violently protesting on the streets of Rajasthan and blocked several rail lines. Police firing on Gujjars began a tit-for-tat cycle of violence between Police and Gujjars. The violence ended with 37 people dead. Their move was opposed by the Meenas, the main ST community in Rajasthan.


title: Reservation in India

text: In 2019, the agitation restarted as Gujjars demanded 5% reservation, and began blocking trains to this effect.


title: Reservation in India

text: Jats have been demanding OBC status since the 1990s. In 2016, they began an agitation to get this status. To this effect they began protesting by blockading roads and lines, but later the protests turned violent. Riots spread to Delhi and western Uttar Pradesh, and even Rajasthan. The epicentre of the violence was in Rothak, and almost ₹34000 crores ($4.8 billion) worth of property was damaged and 30 were killed. Bowing to the pressure, the Haryana government created a special category for Jats and other upper castes called BC, and appointed 10% reservation, but the measure was blocked in court.


title: Reservation in India

text: Beginning in 2015, the Patidar community (better known as Patel) began agitating for OBC status in Gujarat. This movement consisted of massive demonstrations across the state, led by Hardik Patel. Later many of these protests turned violent, resulting in curfews across the state and crores worth of damage. Talks with the government broke down, and the violence restarted. After the Jat agitation began in 2016, the Patidars flared up again and led a march through Gujarat, but protests in several cities turned violent and the Rapid Action Force was sent in.


title: Reservation in India

text: In January 2016, the Kapu community in Andhra Pradesh began leading protests to be classified in Backward Classes. The agitation became violent when in Tuni, Kapu protestors set trains on fire. In 2019, the Telugu Desam Party which had just been made opposition, tabled a bill to have a 5% sub-quota for Kapus out of EWS reservation.


title: Reservation in India

text: Marathas, the dominant caste of Maharashtra, have been agitating for OBC status since the 1990s. In 2016, after the rape and murder of a 15-year old Maratha girl in Kopardi, the Maratha community organized massive protests throughout Maharashtra. Their demands included death for the accused as well as reservations for the Maratha community which makes up 16% of the state's population. Some road blocks turned violent in 2017 and 2018, but overall the protests were peaceful. Their demand was met when the Maharashtra government instituted a special SEBC (Socially and Educationally Backward Classes) category for them with 16% reservation. The Supreme Court of India later however, declared the SEBC reservation for Marathas as unconstitutional.


title: Reservation in India

text: The Union Government tabled the Constitution (One Hundred And Twenty-Fourth Amendment) Bill, 2019 which provided 10% additional quota for the economically weaker sections amongst the erstwhile unreserved category students. The definition of 'economically weaker sections' will be defined by the State from time to time. The constitutional amendment has laid down that they will be restricted to people with household income less than 8 Lakh per annum and those who own agricultural land below five acres. "Business Today" has commented that these criteria cover almost 100 percent of the population. Several petitions have been filed before the Supreme Court of India challenging the legality of this amendment.


title: Reservation in India

text: For OBC's people the following categories are not entitled to take advantage of the reservation system:


title: Reservation in India

text: Institutions of Excellence, research institutions, Institutions of National and Strategic Importance such as Centre for Development of Advanced Computing, Homi Bhabha National Institute and its ten constituent units, the Tata Institute of Fundamental Research (Mumbai), the North Eastern Indira Gandhi Regional Institute of Health and Medical Sciences (Shillong), Physical Research Laboratory (Ahmedabad), the Vikram Sarabhai Space Centre (Thiruvananthapuram) and the Indian Institute of Remote Sensing (Dehradun) do not have reservations for higher education. However Institutes of National Importance such as Indian Institutes of Management (IIMs),Indian Institutes of Technology (IITs), National Institutes of Technology (NIT) and Indian Institute of Information Technology (IIIT) have provision of reservation in admission process for undergraduate and graduate programs.


title: Reservation in India

text: On 27 October 2015, the Supreme Court directed the state and the Central governments to end the regional quota and to ensure that super-specialty medical courses are kept "unreserved, open and free" from any domicile status after the court had allowed petitions files by some MBBS doctors.


title: Reservation in India

text: The term "creamy layer" was first coined in 1974 in the "State of Kerala vs N. M. Thomas" case when a judge said that the "benefits of the reservation shall be snatched away by the top creamy layer of the backward class, thus leaving the weakest among the weak and leaving the fortunate layers to consume the whole cake". The 1992 Indra Sawhney & Others v. Union of India judgement laid down the limits of the state's powers: it upheld the ceiling of 50.21 percent quotas, emphasised the concept of "social backwardness", and prescribed 11 indicators to ascertain backwardness. The judgement also established the concept of qualitative exclusion, such as "creamy layer". The creamy layer applies only to OBCs. The creamy layer criteria were introduced at Rs 1 lakh in 1993 and revised to Rs 2.5 lakh in 2004, ₹4.5 lakh in 2008 and ₹6 lakh in 2013, but now the ceiling has been raised to ₹8 lakh (in September 2017). In October 2015, the National Commission for Backward Classes (NCBC) proposed that a person belonging to OBC with an annual family income of up to ₹15 lakh should be considered as minimum ceiling for OBC. The NCBC also recommended sub-division of OBCs into "backward", "more backward" and "extremely backward" groups and to divide the 27 per cent quota amongst them in proportion to their population, to ensure that stronger OBCs do not corner the quota benefits.


title: Reservation in India

text: Andhra Pradesh state percentage of reservation is around 50%. Including the overall 1/3 reservation for women, 66.66% of seats are reserved in Andhra Pradesh in Education and Government jobs.


title: Reservation in India

text: Assam provides sub quotas for several other communities such as Morans, Mataks and Tea Tribes in medical colleges under the OBC category. In November 2020, Assam's cabinet extended this reservation to Koch-Rajbongshis, Ahoms and Chutias. These six communities are demanding Scheduled Tribe status.


title: Reservation in India

text: First implemented in 1970 by Karpoori Thakur, Bihar has a sub-quota within OBC quota of 18% for Extremely Backward Castes (EBCs) and 3% for Backward Caste women in government jobs and educational institutes. EWS reservation was implemented in 2019.


title: Reservation in India

text: Since Delhi is a Union territory and subject to the Central government, government jobs in Delhi are designated Central Government jobs. In a 2018 Supreme Court decision, it was decided that since Delhi is the capital and no one is an "outsider" there reservations in the territory should follow the all-India pattern. Furthermore, these reserved jobs are open from reserved communities from outside Delhi.


title: Reservation in India

text: In 2014, the quota for OBC reservation was raised from 19.5% to 27%. In June 2019, Goa implemented EWS reservation in jobs and education.


title: Reservation in India

text: Gujarat also implemented a 33% reservation for general category women in government jobs. The government also banned reserved category applicants from competing for general category seats, but this was revoked in 2020. Similarly the women reservation was made cutting across all categories in 2020. Gujarat was one of the first states to implement EWS reservation, which applies to general category candidates with less than ₹8 lakhs income, not including other assets like land.


title: Reservation in India

text: In Haryana OBCs are divided into A, B, C categories, each with 11%, 6% and 6% reservation respectively. Reservations in promotions are different, although still based on population. In 2021, Haryana passed a law mandating 75% reservation in private-sector jobs with incomes less than ₹25,000 for local candidates.


title: Reservation in India

text: In the Scheduled Areas which have a very high percentage of STs, such as Kinnaur and Lahaul and Spiti districts, percentage of ST reserved seats in government jobs are much higher.


title: Reservation in India

text: Uttarakhand has 47% reservation in educational institutions and government jobs. In addition to vertical reservation, the state gives 30% horizontal reservation to women, 5% to the ex-servicemen (ES), 4% to persons with disability (PWD), 2% to the dependants of freedom fighters (DFF), and 5% to the orphans residing in the state-run orphanages.


title: Field (mathematics)

text: In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined and behave as the corresponding operations on rational and real numbers do. A field is thus a fundamental algebraic structure which is widely used in algebra, number theory, and many other areas of mathematics.


title: Field (mathematics)

text: The best known fields are the field of rational numbers, the field of real numbers and the field of complex numbers. Many other fields, such as fields of rational functions, algebraic function fields, algebraic number fields, and "p"-adic fields are commonly used and studied in mathematics, particularly in number theory and algebraic geometry. Most cryptographic protocols rely on finite fields, i.e., fields with finitely many elements.


title: Field (mathematics)

text: The relation of two fields is expressed by the notion of a field extension. Galois theory, initiated by Évariste Galois in the 1830s, is devoted to understanding the symmetries of field extensions. Among other results, this theory shows that angle trisection and squaring the circle cannot be done with a compass and straightedge. Moreover, it shows that quintic equations are, in general, algebraically unsolvable.


title: Field (mathematics)

text: Fields serve as foundational notions in several mathematical domains. This includes different branches of mathematical analysis, which are based on fields with additional structure. Basic theorems in analysis hinge on the structural properties of the field of real numbers. Most importantly for algebraic purposes, any field may be used as the scalars for a vector space, which is the standard general context for linear algebra. Number fields, the siblings of the field of rational numbers, are studied in depth in number theory. Function fields can help describe properties of geometric objects.


title: Field (mathematics)

text: Informally, a field is a set, along with two operations defined on that set: an addition operation written as , and a multiplication operation written as , both of which behave similarly as they behave for rational numbers and real numbers, including the existence of an additive inverse for all elements , and of a multiplicative inverse for every nonzero element . This allows one to also consider the so-called "inverse" operations of subtraction, , and division, , by defining:


title: Field (mathematics)

text: Formally, a field is a set together with two binary operations on called "addition" and "multiplication". A binary operation on is a mapping , that is, a correspondence that associates with each ordered pair of elements of a uniquely determined element of . The result of the addition of and is called the sum of and , and is denoted . Similarly, the result of the multiplication of and is called the product of and , and is denoted or . These operations are required to satisfy the following properties, referred to as "field axioms" (in these axioms, , , and are arbitrary elements of the field ):


title: Field (mathematics)

text: This may be summarized by saying: a field has two operations, called addition and multiplication; it is an abelian group under addition with 0 as the additive identity; the nonzero elements are an abelian group under multiplication with 1 as the multiplicative identity; and multiplication distributes over addition.


title: Field (mathematics)

text: Even more summarized: a field is a commutative ring where formula_1 and all nonzero elements are invertible under multiplication.


title: Field (mathematics)

text: Fields can also be defined in different, but equivalent ways. One can alternatively define a field by four binary operations (addition, subtraction, multiplication, and division) and their required properties. Division by zero is, by definition, excluded. In order to avoid existential quantifiers, fields can be defined by two binary operations (addition and multiplication), two unary operations (yielding the additive and multiplicative inverses respectively), and two nullary operations (the constants and ). These operations are then subject to the conditions above. Avoiding existential quantifiers is important in constructive mathematics and computing. One may equivalently define a field by the same two binary operations, one unary operation (the multiplicative inverse), and two constants and , since and .


title: Field (mathematics)

text: , where and are integers, and . The additive inverse of such a fraction is , and the multiplicative inverse (provided that ) is , which can be seen as follows:


title: Field (mathematics)

text: The abstractly required field axioms reduce to standard properties of rational numbers. For example, the law of distributivity can be proven as follows:


title: Field (mathematics)

text: The real numbers , with the usual operations of addition and multiplication, also form a field. The complex numbers consist of expressions


title: Field (mathematics)

text: Addition and multiplication of real numbers are defined in such a way that expressions of this type satisfy all field axioms and thus hold for . For example, the distributive law enforces


title: Field (mathematics)

text: It is immediate that this is again an expression of the above type, and so the complex numbers form a field. Complex numbers can be geometrically represented as points in the plane, with Cartesian coordinates given by the real numbers of their describing expression, or as the arrows from the origin to these points, specified by their length and an angle enclosed with some distinct direction. Addition then corresponds to combining the arrows to the intuitive parallelogram (adding the Cartesian coordinates), and the multiplication is – less intuitively – combining rotating and scaling of the arrows (adding the angles and multiplying the lengths). The fields of real and complex numbers are used throughout mathematics, physics, engineering, statistics, and many other scientific disciplines.


title: Field (mathematics)

text: In antiquity, several geometric problems concerned the (in)feasibility of constructing certain numbers with compass and straightedge. For example, it was unknown to the Greeks that it is, in general, impossible to trisect a given angle in this way. These problems can be settled using the field of constructible numbers. Real constructible numbers are, by definition, lengths of line segments that can be constructed from the points 0 and 1 in finitely many steps using only compass and straightedge. These numbers, endowed with the field operations of real numbers, restricted to the constructible numbers, form a field, which properly includes the field of rational numbers. The illustration shows the construction of square roots of constructible numbers, not necessarily contained within . Using the labeling in the illustration, construct the segments , , and a semicircle over (center at the midpoint ), which intersects the perpendicular line through in a point , at a distance of exactly formula_4 from when has length one.


title: Field (mathematics)

text: Not all real numbers are constructible. It can be shown that formula_5 is not a constructible number, which implies that it is impossible to construct with compass and straightedge the length of the side of a cube with volume 2, another problem posed by the ancient Greeks.


title: Field (mathematics)

text: In addition to familiar number systems such as the rationals, there are other, less immediate examples of fields. The following example is a field consisting of four elements called , , , and . The notation is chosen such that plays the role of the additive identity element (denoted 0 in the axioms above), and is the multiplicative identity (denoted 1 in the axioms above). The field axioms can be verified by using some more field theory, or by direct computation. For example,


title: Field (mathematics)

text: This field is called a finite field with four elements, and is denoted or . The subset consisting of and (highlighted in red in the tables at the right) is also a field, known as the "binary field" or . In the context of computer science and Boolean algebra, and are often denoted respectively by "false" and "true", and the addition is then denoted XOR (exclusive or). In other words, the structure of the binary field is the basic structure that allows computing with bits.


title: Field (mathematics)

text: One has and . In particular, one may deduce the additive inverse of every element as soon as one knows .


title: Field (mathematics)

text: The axioms of a field imply that it is an abelian group under addition. This group is called the additive group of the field, and is sometimes denoted by when denoting it simply as could be confusing.


title: Field (mathematics)

text: Similarly, the "nonzero" elements of form an abelian group under multiplication, called the multiplicative group, and denoted by or just or .


title: Field (mathematics)

text: A field may thus be defined as set equipped with two operations denoted as an addition and a multiplication such that is an abelian group under addition, is an abelian group under multiplication (where 0 is the identity element of the addition), and multiplication is distributive over addition. Some elementary statements about fields can therefore be obtained by applying general facts of groups. For example, the additive and multiplicative inverses and are uniquely determined by .


title: Field (mathematics)

text: The requirement follows, because 1 is the identity element of a group that does not contain 0. Thus, the trivial ring, consisting of a single element, is not a field.


title: Field (mathematics)

text: In addition to the multiplication of two elements of "F", it is possible to define the product of an arbitrary element of by a positive integer to be the -fold sum


title: Field (mathematics)

text: then is said to have characteristic 0. For example, the field of rational numbers has characteristic 0 since no positive integer is zero. Otherwise, if there "is" a positive integer satisfying this equation, the smallest such positive integer can be shown to be a prime number. It is usually denoted by and the field is said to have characteristic then.


title: Field (mathematics)

text: since all other binomial coefficients appearing in the binomial formula are divisible by . Here, ( factors) is the -th power, i.e., the -fold product of the element . Therefore, the Frobenius map


title: Field (mathematics)

text: is compatible with the addition in (and also with the multiplication), and is therefore a field homomorphism. The existence of this homomorphism makes fields in characteristic quite different from fields of characteristic 0.


title: Field (mathematics)

text: A "subfield" of a field is a subset of that is a field with respect to the field operations of . Equivalently is a subset of that contains , and is closed under addition, multiplication, additive inverse and multiplicative inverse of a nonzero element. This means that , that for all both and are in , and that for all in , both and are in .


title: Field (mathematics)

text: Field homomorphisms are maps between two fields such that , , and , where and are arbitrary elements of . All field homomorphisms are injective. If is also surjective, it is called an isomorphism (or the fields and are called isomorphic).


title: Field (mathematics)

text: A field is called a prime field if it has no proper (i.e., strictly smaller) subfields. Any field contains a prime field. If the characteristic of is (a prime number), the prime field is isomorphic to the finite field introduced below. Otherwise the prime field is isomorphic to .


title: Field (mathematics)

text: "Finite fields" (also called "Galois fields") are fields with finitely many elements, whose number is also referred to as the order of the field. The above introductory example is a field with four elements. Its subfield is the smallest field, because by definition a field has at least two distinct elements .


title: Field (mathematics)

text: The simplest finite fields, with prime order, are most directly accessible using modular arithmetic. For a fixed positive integer , arithmetic "modulo " means to work with the numbers


title: Field (mathematics)

text: The addition and multiplication on this set are done by performing the operation in question in the set of integers, dividing by and taking the remainder as result. This construction yields a field precisely if is a prime number. For example, taking the prime results in the above-mentioned field . For and more generally, for any composite number (i.e., any number which can be expressed as a product of two strictly smaller natural numbers), is not a field: the product of two non-zero elements is zero since in , which, as was explained above, prevents from being a field. The field with elements ( being prime) constructed in this way is usually denoted by .


title: Field (mathematics)

text: Every finite field has elements, where is prime and . This statement holds since may be viewed as a vector space over its prime field. The dimension of this vector space is necessarily finite, say , which implies the asserted statement.


title: Field (mathematics)

text: Such a splitting field is an extension of in which the polynomial has zeros. This means has as many zeros as possible since the degree of is . For , it can be checked case by case using the above multiplication table that all four elements of satisfy the equation , so they are zeros of . By contrast, in , has only two zeros (namely 0 and 1), so does not split into linear factors in this smaller field. Elaborating further on basic field-theoretic notions, it can be shown that two finite fields with the same order are isomorphic. It is thus customary to speak of "the" finite field with elements, denoted by or .


title: Field (mathematics)

text: Historically, three algebraic disciplines led to the concept of a field: the question of solving polynomial equations, algebraic number theory, and algebraic geometry. A first step towards the notion of a field was made in 1770 by Joseph-Louis Lagrange, who observed that permuting the zeros of a cubic polynomial in the expression


title: Field (mathematics)

text: (with being a third root of unity) only yields two values. This way, Lagrange conceptually explained the classical solution method of Scipione del Ferro and François Viète, which proceeds by reducing a cubic equation for an unknown to a quadratic equation for . Together with a similar observation for equations of degree 4, Lagrange thus linked what eventually became the concept of fields and the concept of groups. Vandermonde, also in 1770, and to a fuller extent, Carl Friedrich Gauss, in his "Disquisitiones Arithmeticae" (1801), studied the equation


title: Field (mathematics)

text: for a prime and, again using modern language, the resulting cyclic Galois group. Gauss deduced that a regular -gon can be constructed if . Building on Lagrange's work, Paolo Ruffini claimed (1799) that quintic equations (polynomial equations of degree 5) cannot be solved algebraically; however, his arguments were flawed. These gaps were filled by Niels Henrik Abel in 1824. Évariste Galois, in 1832, devised necessary and sufficient criteria for a polynomial equation to be algebraically solvable, thus establishing in effect what is known as Galois theory today. Both Abel and Galois worked with what is today called an algebraic number field, but conceived neither an explicit notion of a field, nor of a group.


title: Field (mathematics)

text: In 1871 Richard Dedekind introduced, for a set of real or complex numbers that is closed under the four arithmetic operations, the German word "Körper", which means "body" or "corpus" (to suggest an organically closed entity). The English term "field" was introduced by .


title: Field (mathematics)

text: In 1881 Leopold Kronecker defined what he called a "domain of rationality", which is a field of rational fractions in modern terms. Kronecker's notion did not cover the field of all algebraic numbers (which is a field in Dedekind's sense), but on the other hand was more abstract than Dedekind's in that it made no specific assumption on the nature of the elements of a field. Kronecker interpreted a field such as abstractly as the rational function field . Prior to this, examples of transcendental numbers were known since Joseph Liouville's work in 1844, until Charles Hermite (1873) and Ferdinand von Lindemann (1882) proved the transcendence of and , respectively.


title: Field (mathematics)

text: The first clear definition of an abstract field is due to . In particular, Heinrich Martin Weber's notion included the field F. Giuseppe Veronese (1891) studied the field of formal power series, which led to introduce the field of "p"-adic numbers. synthesized the knowledge of abstract field theory accumulated so far. He axiomatically studied the properties of fields and defined many important field-theoretic concepts. The majority of the theorems mentioned in the sections Galois theory, Constructing fields and Elementary notions can be found in Steinitz's work. linked the notion of orderings in a field, and thus the area of analysis, to purely algebraic properties. Emil Artin redeveloped Galois theory from 1928 through 1942, eliminating the dependency on the primitive element theorem.


title: Field (mathematics)

text: A commutative ring is a set, equipped with an addition and multiplication operation, satisfying all the axioms of a field, except for the existence of multiplicative inverses . For example, the integers form a commutative ring, but not a field: the reciprocal of an integer is not itself an integer, unless .


title: Field (mathematics)

text: In the hierarchy of algebraic structures fields can be characterized as the commutative rings in which every nonzero element is a unit (which means every element is invertible). Similarly, fields are the commutative rings with precisely two distinct ideals, and . Fields are also precisely the commutative rings in which is the only prime ideal.


title: Field (mathematics)

text: Given a commutative ring , there are two ways to construct a field related to , i.e., two ways of modifying such that all nonzero elements become invertible: forming the field of fractions, and forming residue fields. The field of fractions of is , the rationals, while the residue fields of are the finite fields .


title: Field (mathematics)

text: Given an integral domain , its field of fractions is built with the fractions of two elements of exactly as Q is constructed from the integers. More precisely, the elements of are the fractions where and are in , and . Two fractions and are equal if and only if . The operation on the fractions work exactly as for rational numbers. For example,


title: Field (mathematics)

text: It is straightforward to show that, if the ring is an integral domain, the set of the fractions form a field.


title: Field (mathematics)

text: The field of the rational fractions over a field (or an integral domain) is the field of fractions of the polynomial ring . The field of Laurent series


title: Field (mathematics)

text: over a field is the field of fractions of the ring of formal power series (in which ). Since any Laurent series is a fraction of a power series divided by a power of (as opposed to an arbitrary power series), the representation of fractions is less important in this situation, though.


title: Field (mathematics)

text: In addition to the field of fractions, which embeds injectively into a field, a field can be obtained from a commutative ring by means of a surjective map onto a field . Any field obtained in this way is a quotient , where is a maximal ideal of . If has only one maximal ideal , this field is called the residue field of .


title: Field (mathematics)

text: The ideal generated by a single polynomial in the polynomial ring (over a field ) is maximal if and only if is irreducible in , i.e., if cannot be expressed as the product of two polynomials in of smaller degree. This yields a field


title: Field (mathematics)

text: For example, is obtained from by adjoining the imaginary unit symbol , which satisfies , where . Moreover, is irreducible over , which implies that the map that sends a polynomial to yields an isomorphism


title: Field (mathematics)

text: Fields can be constructed inside a given bigger container field. Suppose given a field , and a field containing as a subfield. For any element of , there is a smallest subfield of containing and , called the subfield of "F" generated by and denoted . The passage from to is referred to by "adjoining an element" to . More generally, for a subset , there is a minimal subfield of containing and , denoted by .


title: Field (mathematics)

text: The compositum of two subfields and of some field is the smallest subfield of containing both and The compositum can be used to construct the biggest subfield of satisfying a certain property, for example the biggest subfield of , which is, in the language introduced below, algebraic over .


title: Field (mathematics)

text: The notion of a subfield can also be regarded from the opposite point of view, by referring to being a "field extension" (or just extension) of , denoted by


title: Field (mathematics)

text: A basic datum of a field extension is its degree , i.e., the dimension of as an -vector space. It satisfies the formula


title: Field (mathematics)

text: Extensions whose degree is finite are referred to as finite extensions. The extensions and are of degree 2, whereas is an infinite extension.


title: Field (mathematics)

text: A pivotal notion in the study of field extensions are algebraic elements. An element is "algebraic" over if it is a root of a polynomial with coefficients in , that is, if it satisfies a polynomial equation


title: Field (mathematics)

text: For example, the imaginary unit in is algebraic over , and even over , since it satisfies the equation


title: Field (mathematics)

text: A field extension in which every element of is algebraic over is called an algebraic extension. Any finite extension is necessarily algebraic, as can be deduced from the above multiplicativity formula.


title: Field (mathematics)

text: The subfield generated by an element , as above, is an algebraic extension of if and only if is an algebraic element. That is to say, if is algebraic, all other elements of are necessarily algebraic as well. Moreover, the degree of the extension , i.e., the dimension of as an -vector space, equals the minimal degree such that there is a polynomial equation involving , as above. If this degree is , then the elements of have the form


title: Field (mathematics)

text: For example, the field of Gaussian rationals is the subfield of consisting of all numbers of the form where both and are rational numbers: summands of the form (and similarly for higher exponents) don't have to be considered here, since can be simplified to .


title: Field (mathematics)

text: The above-mentioned field of rational fractions , where is an indeterminate, is not an algebraic extension of since there is no polynomial equation with coefficients in whose zero is . Elements, such as , which are not algebraic are called transcendental. Informally speaking, the indeterminate and its powers do not interact with elements of . A similar construction can be carried out with a set of indeterminates, instead of just one.


title: Field (mathematics)

text: Once again, the field extension discussed above is a key example: if is not algebraic (i.e., is not a root of a polynomial with coefficients in ), then is isomorphic to . This isomorphism is obtained by substituting to in rational fractions.


title: Field (mathematics)

text: A subset of a field is a transcendence basis if it is algebraically independent (don't satisfy any polynomial relations) over and if is an algebraic extension of . Any field extension has a transcendence basis. Thus, field extensions can be split into ones of the form (purely transcendental extensions) and algebraic extensions.


title: Field (mathematics)

text: A field is algebraically closed if it does not have any strictly bigger algebraic extensions or, equivalently, if any polynomial equation


title: Field (mathematics)

text: has a solution . By the fundamental theorem of algebra, is algebraically closed, i.e., "any" polynomial equation with complex coefficients has a complex solution. The rational and the real numbers are "not" algebraically closed since the equation


title: Field (mathematics)

text: does not have any rational or real solution. A field containing is called an "algebraic closure" of if it is algebraic over (roughly speaking, not too big compared to ) and is algebraically closed (big enough to contain solutions of all polynomial equations).


title: Field (mathematics)

text: By the above, is an algebraic closure of . The situation that the algebraic closure is a finite extension of the field is quite special: by the Artin-Schreier theorem, the degree of this extension is necessarily 2, and is elementarily equivalent to . Such fields are also known as real closed fields.


title: Field (mathematics)

text: Any field has an algebraic closure, which is moreover unique up to (non-unique) isomorphism. It is commonly referred to as "the" algebraic closure and denoted . For example, the algebraic closure of is called the field of algebraic numbers. The field is usually rather implicit since its construction requires the ultrafilter lemma, a set-theoretic axiom that is weaker than the axiom of choice. In this regard, the algebraic closure of , is exceptionally simple. It is the union of the finite fields containing (the ones of order ). For any algebraically closed field of characteristic 0, the algebraic closure of the field of Laurent series is the field of Puiseux series, obtained by adjoining roots of .


title: Field (mathematics)

text: Since fields are ubiquitous in mathematics and beyond, several refinements of the concept have been adapted to the needs of particular mathematical areas.


title: Field (mathematics)

text: A field "F" is called an "ordered field" if any two elements can be compared, so that and whenever and . For example, the real numbers form an ordered field, with the usual ordering . The Artin-Schreier theorem states that a field can be ordered if and only if it is a formally real field, which means that any quadratic equation


title: Field (mathematics)

text: only has the solution . The set of all possible orders on a fixed field is isomorphic to the set of ring homomorphisms from the Witt ring of quadratic forms over , to .


title: Field (mathematics)

text: whose value is greater than that element, that is, there are no infinite elements. Equivalently, the field contains no infinitesimals (elements smaller than all rational numbers); or, yet equivalent, the field is isomorphic to a subfield of .


title: Field (mathematics)

text: An ordered field is Dedekind-complete if all upper bounds, lower bounds (see Dedekind cut) and limits, which should exist, do exist. More formally, each bounded subset of is required to have a least upper bound. Any complete field is necessarily Archimedean, since in any non-Archimedean field there is neither a greatest infinitesimal nor a least positive rational, whence the sequence , every element of which is greater than every infinitesimal, has no limit.


title: Field (mathematics)

text: Since every proper subfield of the reals also contains such gaps, is the unique complete ordered field, up to isomorphism. Several foundational results in calculus follow directly from this characterization of the reals.


title: Field (mathematics)

text: The hyperreals form an ordered field that is not Archimedean. It is an extension of the reals obtained by including infinite and infinitesimal numbers. These are larger, respectively smaller than any real number. The hyperreals form the foundational basis of non-standard analysis.


title: Field (mathematics)

text: Another refinement of the notion of a field is a topological field, in which the set is a topological space, such that all operations of the field (addition, multiplication, the maps and ) are continuous maps with respect to the topology of the space.


title: Field (mathematics)

text: The completion of is another field in which, informally speaking, the "gaps" in the original field are filled, if there are any. For example, any irrational number , such as , is a "gap" in the rationals in the sense that it is a real number that can be approximated arbitrarily closely by rational numbers , in the sense that distance of and given by the absolute value is as small as desired.


title: Field (mathematics)

text: The following table lists some examples of this construction. The fourth column shows an example of a zero sequence, i.e., a sequence whose limit (for ) is zero.


title: Field (mathematics)

text: The field is used in number theory and -adic analysis. The algebraic closure carries a unique norm extending the one on , but is not complete. The completion of this algebraic closure, however, is algebraically closed. Because of its rough analogy to the complex numbers, it is sometimes called the field of complex p-adic numbers and is denoted by .


title: Field (mathematics)

text: These two types of local fields share some fundamental similarities. In this relation, the elements and (referred to as uniformizer) correspond to each other. The first manifestation of this is at an elementary level: the elements of both fields can be expressed as power series in the uniformizer, with coefficients in . (However, since the addition in is done using carrying, which is not the case in , these fields are not isomorphic.) The following facts show that this superficial similarity goes much deeper:


title: Field (mathematics)

text: Differential fields are fields equipped with a derivation, i.e., allow to take derivatives of elements in the field. For example, the field R("X"), together with the standard derivative of polynomials forms a differential field. These fields are central to differential Galois theory, a variant of Galois theory dealing with linear differential equations.


title: Field (mathematics)

text: Galois theory studies algebraic extensions of a field by studying the symmetry in the arithmetic operations of addition and multiplication. An important notion in this area is that of finite Galois extensions , which are, by definition, those that are separable and normal. The primitive element theorem shows that finite separable extensions are necessarily simple, i.e., of the form


title: Field (mathematics)

text: where is an irreducible polynomial (as above). For such an extension, being normal and separable means that all zeros of are contained in and that has only simple zeros. The latter condition is always satisfied if has characteristic 0.


title: Field (mathematics)

text: For a finite Galois extension, the Galois group is the group of field automorphisms of that are trivial on (i.e., the bijections that preserve addition and multiplication and that send elements of to themselves). The importance of this group stems from the fundamental theorem of Galois theory, which constructs an explicit one-to-one correspondence between the set of subgroups of and the set of intermediate extensions of the extension . By means of this correspondence, group-theoretic properties translate into facts about fields. For example, if the Galois group of a Galois extension as above is not solvable (cannot be built from abelian groups), then the zeros of "cannot" be expressed in terms of addition, multiplication, and radicals, i.e., expressions involving formula_12. For example, the symmetric groups is not solvable for . Consequently, as can be shown, the zeros of the following polynomials are not expressible by sums, products, and radicals. For the latter polynomial, this fact is known as the Abel–Ruffini theorem:


title: Field (mathematics)

text: The tensor product of fields is not usually a field. For example, a finite extension of degree is a Galois extension if and only if there is an isomorphism of -algebras


title: Field (mathematics)

text: This fact is the beginning of Grothendieck's Galois theory, a far-reaching extension of Galois theory applicable to algebro-geometric objects.


title: Field (mathematics)

text: Basic invariants of a field include the characteristic and the transcendence degree of over its prime field. The latter is defined as the maximal number of elements in that are algebraically independent over the prime field. Two algebraically closed fields and are isomorphic precisely if these two data agree. This implies that any two uncountable algebraically closed fields of the same cardinality and the same characteristic are isomorphic. For example, and are isomorphic (but "not" isomorphic as topological fields).


title: Field (mathematics)

text: In model theory, a branch of mathematical logic, two fields and are called elementarily equivalent if every mathematical statement that is true for is also true for and conversely. The mathematical statements in question are required to be first-order sentences (involving 0, 1, the addition and multiplication). A typical example, for , "n" an integer, is


title: Field (mathematics)

text: The Lefschetz principle states that is elementarily equivalent to any algebraically closed field of characteristic zero. Moreover, any fixed statement holds in if and only if it holds in any algebraically closed field of sufficiently high characteristic.


title: Field (mathematics)

text: If is an ultrafilter on a set , and is a field for every in , the ultraproduct of the with respect to is a field. It is denoted by


title: Field (mathematics)

text: since it behaves in several ways as a limit of the fields : Łoś's theorem states that any first order statement that holds for all but finitely many , also holds for the ultraproduct. Applied to the above sentence , this shows that there is an isomorphism


title: Field (mathematics)

text: The Ax–Kochen theorem mentioned above also follows from this and an isomorphism of the ultraproducts (in both cases over all primes )


title: Field (mathematics)

text: In addition, model theory also studies the logical properties of various other types of fields, such as real closed fields or exponential fields (which are equipped with an exponential function ).


title: Field (mathematics)

text: For fields that are not algebraically closed (or not separably closed), the absolute Galois group is fundamentally important: extending the case of finite Galois extensions outlined above, this group governs "all" finite separable extensions of . By elementary means, the group can be shown to be the Prüfer group, the profinite completion of . This statement subsumes the fact that the only algebraic extensions of are the fields for , and that the Galois groups of these finite extensions are given by


title: Field (mathematics)

text: A description in terms of generators and relations is also known for the Galois groups of -adic number fields (finite extensions of ).


title: Field (mathematics)

text: Representations of Galois groups and of related groups such as the Weil group are fundamental in many branches of arithmetic, such as the Langlands program. The cohomological study of such representations is done using Galois cohomology. For example, the Brauer group, which is classically defined as the group of central simple -algebras, can be reinterpreted as a Galois cohomology group, namely


title: Field (mathematics)

text: The norm residue isomorphism theorem, proved around 2000 by Vladimir Voevodsky, relates this to Galois cohomology by means of an isomorphism


title: Field (mathematics)

text: Algebraic K-theory is related to the group of invertible matrices with coefficients the given field. For example, the process of taking the determinant of an invertible matrix leads to an isomorphism K("F") = "F". Matsumoto's theorem shows that K("F") agrees with K("F"). In higher degrees, K-theory diverges from Milnor K-theory and remains hard to compute in general.


title: Field (mathematics)

text: has a unique solution in a field , namely formula_16 This immediate consequence of the definition of a field is fundamental in linear algebra. For example, it is an essential ingredient of Gaussian elimination and of the proof that any vector space has a basis.


title: Field (mathematics)

text: The theory of modules (the analogue of vector spaces over rings instead of fields) is much more complicated, because the above equation may have several or no solutions. In particular systems of linear equations over a ring are much more difficult to solve than in the case of fields, even in the specially simple case of the ring formula_17 of the integers.


title: Field (mathematics)

text: in a (large) finite field can be performed much more efficiently than the discrete logarithm, which is the inverse operation, i.e., determining the solution to an equation


title: Field (mathematics)

text: In elliptic curve cryptography, the multiplication in a finite field is replaced by the operation of adding points on an elliptic curve, i.e., the solutions of an equation of the form


title: Field (mathematics)

text: Functions on a suitable topological space into a field can be added and multiplied pointwise, e.g., the product of two functions is defined by the product of their values within the domain:


title: Field (mathematics)

text: For having a "field" of functions, one must consider algebras of functions that are integral domains. In this case the ratios of two functions, i.e., expressions of the form


title: Field (mathematics)

text: This occurs in two main cases. When is a complex manifold . In this case, one considers the algebra of holomorphic functions, i.e., complex differentiable functions. Their ratios form the field of meromorphic functions on .


title: Field (mathematics)

text: The function field of an algebraic variety (a geometric object defined as the common zeros of polynomial equations) consists of ratios of regular functions, i.e., ratios of polynomial functions on the variety. The function field of the -dimensional space over a field is , i.e., the field consisting of ratios of polynomials in indeterminates. The function field of is the same as the one of any open dense subvariety. In other words, the function field is insensitive to replacing by a (slightly) smaller subvariety.


title: Field (mathematics)

text: The function field is invariant under isomorphism and birational equivalence of varieties. It is therefore an important tool for the study of abstract algebraic varieties and for the classification of algebraic varieties. For example, the dimension, which equals the transcendence degree of , is invariant under birational equivalence. For curves (i.e., the dimension is one), the function field is very close to : if is smooth and proper (the analogue of being compact), can be reconstructed, up to isomorphism, from its field of functions. In higher dimension the function field remembers less, but still decisive information about . The study of function fields and their geometric meaning in higher dimensions is referred to as birational geometry. The minimal model program attempts to identify the simplest (in a certain precise sense) algebraic varieties with a prescribed function field.


title: Field (mathematics)

text: They are, by definition, number fields (finite extensions of ) or function fields over (finite extensions of ). As for local fields, these two types of fields share several similar features, even though they are of characteristic 0 and positive characteristic, respectively. This function field analogy can help to shape mathematical expectations, often first by understanding questions about function fields, and later treating the number field case. The latter is often more difficult. For example, the Riemann hypothesis concerning the zeros of the Riemann zeta function (open as of 2017) can be regarded as being parallel to the Weil conjectures (proven in 1974 by Pierre Deligne).


title: Field (mathematics)

text: Cyclotomic fields are among the most intensely studied number fields. They are of the form , where is a primitive -th root of unity, i.e., a complex number satisfying and for all . For being a regular prime, Kummer used cyclotomic fields to prove Fermat's Last Theorem, which asserts the non-existence of rational nonzero solutions to the equation


title: Field (mathematics)

text: Local fields are completions of global fields. Ostrowski's theorem asserts that the only completions of , a global field, are the local fields and . Studying arithmetic questions in global fields may sometimes be done by looking at the corresponding questions locally. This technique is called the local-global principle. For example, the Hasse–Minkowski theorem reduces the problem of finding rational solutions of quadratic equations to solving these equations in and , whose solutions can easily be described.


title: Field (mathematics)

text: Unlike for local fields, the Galois groups of global fields are not known. Inverse Galois theory studies the (unsolved) problem whether any finite group is the Galois group for some number field . Class field theory describes the abelian extensions, i.e., ones with abelian Galois group, or equivalently the abelianized Galois groups of global fields. A classical statement, the Kronecker–Weber theorem, describes the maximal abelian extension of : it is the field


title: Field (mathematics)

text: obtained by adjoining all primitive -th roots of unity. Kronecker's Jugendtraum asks for a similarly explicit description of of general number fields . For imaginary quadratic fields, formula_19, , the theory of complex multiplication describes using elliptic curves. For general number fields, no such explicit description is known.


title: Field (mathematics)

text: In addition to the additional structure that fields may enjoy, fields admit various other related notions. Since in any field 0 ≠ 1, any field has at least two elements. Nonetheless, there is a concept of field with one element, which is suggested to be a limit of the finite fields , as tends to 1. In addition to division rings, there are various other weaker algebraic structures related to fields such as quasifields, near-fields and semifields.


title: Field (mathematics)

text: There are also proper classes with field structure, which are sometimes called Fields, with a capital F. The surreal numbers form a Field containing the reals, and would be a field except for the fact that they are a proper class, not a set. The nimbers, a concept from game theory, form such a Field as well.


title: Field (mathematics)

text: Dropping one or several axioms in the definition of a field leads to other algebraic structures. As was mentioned above, commutative rings satisfy all field axioms except for the existence of multiplicative inverses. Dropping instead commutativity of multiplication leads to the concept of a "division ring" or "skew field"; sometimes associativity is weakened as well. The only division rings that are finite-dimensional -vector spaces are itself, (which is a field), and the quaternions (in which multiplication is non-commutative). This result is known as the Frobenius theorem. The octonions , for which multiplication is neither commutative nor associative, is a normed alternative division algebra, but is not a division ring. This fact was proved using methods of algebraic topology in 1958 by Michel Kervaire, Raoul Bott, and John Milnor. The non-existence of an odd-dimensional division algebra is more classical. It can be deduced from the hairy ball theorem illustrated at the right.


title: Prawn

text: Prawn is a common name for small aquatic crustaceans with an exoskeleton and ten legs (which is a member of the order decapoda), some of which can be eaten.


title: Prawn

text: The term "prawn" is used particularly in the United Kingdom, Ireland, and Commonwealth nations, for large swimming crustaceans or shrimp, especially those with commercial significance in the fishing industry. Shrimp that are present in this category often belong to the suborder Dendrobranchiata. In North America, the term is used less frequently, typically for freshwater shrimp. The terms shrimp and prawn themselves lack scientific standing. Over the years, the way they are used has changed, and in contemporary usage the terms are almost interchangeable.


title: Prawn

text: The terms shrimp and prawn originated in Britain. In the use of common names for species, shrimp is applied to smaller species, particularly species that are dorsoventrally depressed (wider than deep) with a shorter rostrum. It is the only term used for species in the family Crangonidae, such as the common shrimp or brown shrimp, "Crangon crangon". Prawn is never applied to very small species. It is applied to most of the larger forms, particularly species that are laterally compressed (deeper than wide) and have a long rostrum. However, the terms are not used consistently. For example, some authors refer to "Pandalus montagui" as an Aesop shrimp, while others refer to it as an Aesop prawn.


title: Prawn

text: Commonwealth countries, and Ireland, tend to follow British usage. Some exceptions occur in Australia, where some authors refer to small species of the Palaemonidae as prawns and call the Alpheidae pistol shrimp. Other Australian authors have given the name banded coral shrimp to the prawn-like "Stenopus hispidus" and listed "the Processidae and Atyidae as shrimps, the Hippolytidae, Alpheidae, Pandalidae and Campylonotoidea as prawns". New Zealand broadly follows British usage. A rule of thumb given by some New Zealand authors states: "In common usage, shrimp are small, some three inches or less in length, taken for food by netting, usually from shallow water. Prawn are larger, up to 12 inches long, taken by trapping and trawling." In Canada, the terms are often used interchangeably as in New Zealand (larger species are prawn and smaller are often shrimp), but regional variations exist. In western provinces, prawn is almost exclusively the general term. South Africa and the former British colonies in Asia also seem to generally follow British usage.


title: Prawn

text: Shrimp is the more general term in the United States. The term prawn is less commonly used in the United States, being applied mainly to larger shrimp and those living in fresh water.


title: Scarface (1932 film)

text: Scarface (also known as Scarface: The Shame of the Nation and The Shame of a Nation) is a 1932 American pre-Code gangster film directed by Howard Hawks and produced by Hawks and Howard Hughes. The screenplay, by Ben Hecht, is based loosely on the 1929 novel by Armitage Trail which was inspired by Al Capone. The film stars Paul Muni as Italian immigrant gangster Antonio "Tony" Camonte, a gangster who violently rises through the Chicago gangland, with a supporting cast that includes George Raft and Boris Karloff. Camonte's rise to power dovetails with his relentless pursuit of his boss's mistress while his own sister pursues his best hitman. In an overt tie to the life of Capone, one scene depicts a version of the Saint Valentine's Day Massacre.


title: Scarface (1932 film)

text: After Hughes purchased the rights to Trail's novel, Hughes quickly selected Hawks to direct and Hecht to write the film's screenplay. Beginning in January 1931, Hecht wrote the script over an eleven-day period. "Scarface" was produced before the introduction of the Production Code in 1934, which enforced regulations on film content. However, the Hays Code, a more lenient precursor, called for major alterations, including a prologue condemning gangsters, an alternate ending to more clearly reprehend Camonte, and the alternative title "The Shame of a Nation". The censors believed the film glorified violence and crime. These changes delayed the film by a year, though some showings retained the original ending. Modern showings of the film have the original ending, though some DVD releases also include the alternate ending as a feature; these versions maintain the changes Hughes and Hawks were required to make for approval by the Hays Office. No completely unaltered version was known to exist until the limited edition set of "Scarface" (1983) was released on October 15, 2019.


title: Scarface (1932 film)

text: Audience reception was positive, but censors banned the film in several cities and states, forcing Hughes to remove it from circulation and store it in his vault. The rights to the film were recovered after Hughes's death in the 1970s. Alongside "Little Caesar" and "The Public Enemy" (both 1931), "Scarface" is regarded as among the most significant gangster films, and greatly influenced the genre.


title: Scarface (1932 film)

text: "Scarface" was added to the National Film Registry in 1994 by the Library of Congress. In 2008, the American Film Institute listed "Scarface" as the sixth-best gangster film. It was remade as the 1983 film of the same title starring Al Pacino.


title: Scarface (1932 film)

text: In 1920s Chicago, Italian immigrant and notorious thug Antonio "Tony" Camonte works as a bodyguard for crime lord "Big" Louis Costillo. Siding with Costillo's disgruntled lieutenant John "Johnny" Lovo, Tony guns down his boss. Lovo takes over Costillo's territory in the South Side and has Tony and his associates, Angelo and Guino "Little Boy" Rinaldo, set up a lucrative bootlegging operation selling illegal beer to all of the bars there.


title: Scarface (1932 film)

text: Tony urges Lovo to start moving in on the North Side, where the bootlegging is controlled by the Irish gangs of gangster O'Hara; Lovo refuses, ordering Tony to leave the North Side alone. Tony ignores these orders and starts attacking O'Hara's businesses while expanding his rackets to the North. Before long, Lovo is forced out of his position as Tony wins over their gang with his success.


title: Scarface (1932 film)

text: Meanwhile, Tony pursues Johnny's girlfriend Poppy. At first, she is dismissive of him, but pays him more attention as his reputation rises and he starts flaunting his wealth. She visits his "gaudy" apartment where he shows her his view of an electric billboard advertising Cook's Tours, which features the slogan which inspires him: "The World Is Yours".


title: Scarface (1932 film)

text: Tony finally gets rid of O'Hara by having Guino assassinate him. O'Hara's successor, Tom Gaffney, declares war on the South Side and attempts to kill Tony in a restaurant with tommy guns – which an excited Tony quickly arms his own men with. The war results in Gaffney's gang being killed off one by one until he's forced to go into hiding. A group of prominent citizens, including the police chief, vow to bring Tony down for all the carnage and bloodshed he has inflicted on the city.


title: Scarface (1932 film)

text: During a night out at the theater, Tony learns that Gaffney and his entourage are at a nearby bowling alley. Leaving Angelo behind to watch the rest of the show, Tony personally kills Gaffney. Lovo's anger at Tony finally boils over when Tony openly flirts and dances with Poppy in front of him at dinner. Tony sees his beloved sister Francesca "Cesca" dancing with a stranger and takes her to his mother's home by force before hitting and yelling at her. A crew of gunmen later try to assassinate him, but he runs them off the road with his bulletproof car.


title: Scarface (1932 film)

text: Suspecting Lovo's involvement, Tony goes to his office after bribing one of Lovo's men to call him and pretend to be part of the hit crew. When Lovo hangs up after claiming that he must have gotten a wrong number, Tony forces him to confess to the hit and then has Guino kill him. Tony, now the undisputed ruler of the city's underworld, takes Poppy on an expensive vacation to Florida to escape the police and media attention, while Cesca secretly visits Guino at Tony's office.


title: Scarface (1932 film)

text: Cesca slips inside, planning to kill her brother, but then gives in and admits her love for him. Tony and Cesca arm themselves and Tony shoots at the police from the window, laughing maniacally. Moments later, however, Cesca is killed by a stray bullet. Calling Cesca's name as the apartment fills with tear gas, Tony stumbles down the stairs just as the police break down his door. Tony pleads for his life but makes a break for it, resulting in the officers outside shooting him multiple times. He stumbles for a moment, falls in the gutter and dies. Above the sounds of cheering, the electric billboard blazes "The World Is Yours".


title: Scarface (1932 film)

text: Business tycoon Howard Hughes, then involved in film-making, wanted a box office hit after the success of his 1931 film "The Front Page". Gangster films were topical in the early 1930s in the age of Prohibition, and Hughes wanted to make a film based on the life of gangster Al Capone superior to all other films in the genre. He was advised against making the film, as the genre was crowded; "Little Caesar" starring Edward G. Robinson and "The Public Enemy" starring James Cagney were already box-office successes, and Warner Bros. claimed nothing new could be done with the gangster genre. Furthermore, industry censors such as the Hays Office were becoming concerned with the glamorization of crime in media.


title: Scarface (1932 film)

text: Hughes bought the rights to Armitage Trail's novel "Scarface", inspired by the life of Capone. Trail wrote for a number of detective story magazines during the early 1920s, but died of a heart attack at the age of 28, shortly before the release of "Scarface". Hughes hired Fred Pasley, a New York reporter and authority on Capone, as a writer. Hughes asked Ben Hecht, who in 1929 had won the first Academy Award for Best Original Screenplay for his silent crime film "Underworld", to be head writer. Suspicious of Hughes as an employer, Hecht requested a daily salary of $1,000, to be paid every day at six o'clock. Hecht claimed he would only waste a day's labor if Hughes turned out to be a fraud.


title: Scarface (1932 film)

text: Hughes wanted film director Howard Hawks to direct and co-produce. This surprised Hawks, as the two had never been friendly; Hughes had filed a lawsuit against Howard Hawks in July 1930, alleging that Hawks's film "The Dawn Patrol" had plagiarized his film "Hell's Angels". Over a game of golf, Hughes promised to drop the lawsuit (irrelevant as it had already been dismissed by the judge), and by the eighteenth hole, Hawks had become interested in directing the film. He became more convinced when he discovered Hecht would be the head writer. Hecht and Hawks worked together well, intending to portray the Capone character as of the Borgia Family, including the suggestion of incest between the main character and his sister, present in Trail's novel.


title: Scarface (1932 film)

text: Hecht wrote the screenplay over eleven days in January 1931, adapted from Trail's novel. Additional writing was provided by Fred Pasley and W.R. Burnett, author of the novel "Little Caesar," upon which the film "Little Caesar" was based. Pasley's contributions included elements of the book "Al Capone: Biography of a Self-Made Man;" the book contains a barbershop scene with Capone similar to the introduction of Tony Camonte in the film. Pasley was not credited for his work on the screenplay. John Lee Mahin and Seton I. Miller rewrote the script for continuity and dialogue.


title: Scarface (1932 film)

text: Because there were five writers, it is difficult to distinguish which components were contributed by which writer; however, the ending of "Scarface" is similar to Hecht's first gangster film "Underworld," in which gangster Bull Weed traps himself in his apartment with his lover and fires at the hordes of police outside, and thus was likely a Hecht contribution.


title: Scarface (1932 film)

text: The film version of "Scarface" bears little resemblance to the novel. Though the film contains the same major characters, plot points, and incestual undertones, changes were made to reduce the length and the number of characters, and to satisfy the requests of censorship offices. To make gangsters appear less admirable, Tony's character was made to appear less intelligent and more brutish than in the novel. Similarly, the sibling relationship between Tony and the police officer was removed to avoid depicting police corruption.


title: Scarface (1932 film)

text: Both the film and novel are loosely based upon the life of gangster Al Capone, whose nickname was "Scarface". The names of characters and locations were changed only minimally. Capone became Camonte, Torrio became Lovo, and Moran became Doran. In some early scripts, Colosimo was Colisimo and O'Bannion was Bannon, but the names were changed to Costillo and O'Hara respectively. This, including other alterations made to characters and other identifying locations to maintain anonymity, were due to censorship and Hawks's concern about the overuse of historical details.


title: Scarface (1932 film)

text: Ben Hecht had met Capone and "knew a lot about Chicago", so he did no research for the script. According to Hecht, while he worked on the script, Capone sent two men to visit him in Hollywood to make sure the film was not based on Capone's life. He told them the Scarface character was a parody of numerous people, and that the title was chosen as it was intriguing. The two left Hecht alone.


title: Scarface (1932 film)

text: The references to Capone and actual events from the Chicago gang wars were obvious to audiences at the time. Muni's character had a scar similar to Capone's, received in similar fights. The police in the film mention Camonte is a member of the Five Points Gang in Brooklyn, of which Capone was a known member. Tony kills his boss "Big Louis" Costillo in the lobby of his club; Capone was involved in the murder of his first boss "Big Jim" Colosimo in 1920. Rival boss O'Hara is murdered in his flower shop; Capone's men murdered Dean O'Bannion in his flower shop in 1924. The assassination of seven men in a garage, with two of the gunmen costumed as police officers, mirrors the St. Valentine's Day Massacre of 1929. The leader of this rival gang narrowly escapes the shooting, as did gang leader Bugs Moran. The film opens at the intersection of 22nd Street and Wabash Avenue in the middle of Capone's South Side, the site of many Capone's crimes.


title: Scarface (1932 film)

text: Despite the clear references to Capone, Capone was rumored to have liked the film so much he owned a print of it. However, this was likely an exaggerated claim by Hawks as Capone was imprisoned in Atlanta for tax evasion during the film's release.


title: Scarface (1932 film)

text: Hawks and Hughes found casting difficult as most actors were under contract and studios were reluctant to allow their artists to freelance for independent producers. Producer Irving Thalberg suggested Clark Gable, but Hawks believed Gable was a personality, not an actor. After seeing Paul Muni on Broadway, talent agent Al Rosen suggested him for the lead role. Muni initially declined, feeling he was not physically suited for the role, but after reading the script, his wife Bella convinced him to take it. After a test run in New York, Hughes, Hawks, and Hecht approved Muni for the role.


title: Scarface (1932 film)

text: Boris Karloff was cast as Irish gangster Gaffney, listed on a theatrical release poster as "Boris 'Frankenstein' Karloff". Jack La Rue was cast as Tony Camonte's sidekick Guino Rinaldo (modeled after Al Capone's bodyguard Frank Rio) but as he was taller than Muni, Hawks worried he would overshadow Muni's tough Scarface persona. He was replaced with George Raft, a struggling actor at the time, after Hawks encountered him at a prizefight. Raft had played an almost identical part the previous year as his feature film debut in "Quick Millions", a gangster film starring Spencer Tracy, but the "Scarface" role would catapult Raft to stardom.


title: Scarface (1932 film)

text: Though Karen Morley was under contract at MGM, Hawks was close with MGM studio executive Eddie Mannix, who loaned out Morley for the film. She was reportedly given the choice between the role of Poppy or Cesca. Though Cesca was the stronger role, she chose Poppy as she felt Cesca would be a better fit for her friend Ann Dvorak. She considered this "probably the nicest thing [she] did in [her] life". Morley invited 20-year-old Dvorak to a party at Hawks' house to introduce them. According to Hawks, at the party, Dvorak zeroed in on George Raft who played her love interest. He initially declined her invitation to dance. She tried to dance in front of him in order to lure him; eventually, he gave in, and their dance together stopped the party. After this event, Hawks was interested in casting her but had reservations about her lack of experience. After a screen test, he gave her the part, and MGM was willing to release her from her contract as a chorus girl. Dvorak had to both receive permission from her mother Anna Lehr and to win a petition presented to the Superior Court to be able to sign on with Howard Hawks as a minor.


title: Scarface (1932 film)

text: Filming lasted six months, which was long for films made in the early 1930s. Howard Hughes remained off-set to avoid interfering with the filming of the movie. Hughes urged Hawks to make the film as visually exciting as possible by adding car chases, crashes, and machine-gun fire. Hawks shot the film at three different locations: Metropolitan Studios, Harold Lloyd Studios and the Mayan Theater in Los Angeles. Filming took three months with the cast and crew working seven days a week. For the most violent scene of the film in the restaurant, Hawks cleared the set to avoid harming extras and had the set fired on by machine guns. The actors acted out the scene in front of a screen with the shooting projected in the back, so as everyone crowded under the tables in the restaurant, the room appeared to be simultaneously under fire.


title: Scarface (1932 film)

text: During filming, Hawks and Hughes met with the Hays Office to discuss revisions. Despite that, "Scarface" was filmed and put together quickly. In September 1931, a rough cut of the film was screened for the California Crime Commission and police officials, neither of whom thought the movie was a dangerous influence for audiences or would elicit a criminal response. Irving Thalberg was given an advanced screening and was impressed by the film. Despite the positive feedback the film was given, the Hays Office was insistent on changes before final approval.


title: Scarface (1932 film)

text: "Scarface" was produced and filmed during Pre-Code era of Hollywood, which spanned from 1930 to 1934. The Pre-Code era is characterized by its informal and haphazard screening and regulation of film content, before the establishment of the Production Code Administration (PCA) on July 1, 1934. Before the influence of the PCA, censorship was overseen by the Motion Pictures Producers and Distributors of America (MPPDA). In 1930, Will Hays, the chairman of the MPPDA, attempted to regulate the content of movies; the MPPDA became known as the Hays Office. The goal of the Hays Office was to censor nudity, sexuality, drug use and crime. More specific to "Scarface", the Hays Office wanted to avoid the sympathetic portrayal of crime by either showing criminals recognizing the error of their ways or showing criminals get punished. The Hays Office, however, did not have authority to remove material from a film until the MPPDA officially pledged to adhere to the Production Code in 1934, so they relied on delaying film release and lobbying to remove scenes or prevent movies from being produced. Films evaded the Hays Office by adding extremely suggestive scenes so they could remove them and satisfy the Hays Office enough that they wouldn't notice the lesser immoralities that remained in the film.


title: Scarface (1932 film)

text: J.E. Smyth described "Scarface" as "one of the most highly censored films in Hollywood history." Howard Hawks believed the Hays Office had personal vendettas against the movie, while Hughes believed the censorship was due to "ulterior and political motives" of corrupt politicians. However, James Wingate of the New York censor boards rebutted that Hughes was preoccupied with "box office publicity" in producing the film. After repeated demands for a script rewrite from the Hays Office, Hughes ordered Hawks to shoot the film: "Screw the Hays Office, make it as realistic, and grisly as possible." The Hays Office was outraged by "Scarface" when they screened it. According to the Hays Office, "Scarface" violated the Code, because the film elicited sympathy for Muni's character and it revealed to youth a successful method of crime. The Hays office called for scenes to be deleted, scenes to be added to condemn gangsterism, and a different ending. They believed Tony's death at the end of the film was too glorifying. In addition to the violence, the MPPDA felt an inappropriate relationship between the main character and his sister was too overt, especially when he holds her in his arms after he slaps her and tears her dress; they ordered this scene be deleted. Hughes, in order to receive the MPPDA's approval, deleted the more violent scenes, added a prologue to condemn gangsterism, and wrote a new ending.


title: Scarface (1932 film)

text: In addition, a couple of scenes were added to overtly condemn gangsterism, such as a scene in which a newspaper publisher looks at the screen and directly admonishes the government and the public for their lack of action in fighting against mob violence and a scene in which the chief detective denounces the glorification of gangsters. Hawks refused to shoot the extra scenes and the alternate ending. They were directed by Richard Rossen, earning Rossen the title of "co-director". Hughes was instructed to change the title to "The Menace", "Shame of the Nation" or "Yellow" to clarify the subject of the film; after months of haggling, he compromised with the title "Scarface, Shame of the Nation" and by adding a foreword condemning the "gangster" in a general sense. Hughes made an attempt to release the film under the title "The Scar" when the original title was disallowed by the Hays office. Besides the title, the term "Scarface" was removed from the film. In the scene where Tony kills Rinaldo, Cesca says the word "murderer", but she can be seen mouthing the word "Scarface".


title: Scarface (1932 film)

text: The original script had Tony's mother loving her son unconditionally, praising his lifestyle, and even accepting money and gifts from him. In addition, there was a politician who, despite campaigning against gangsters on the podium, is shown partying with them after hours. The script ends with Tony staying in the building, unaffected by tear gas and a multitude of bullets fired at him. After the building is on fire, Tony is forced to exit, guns blazing. He is sprayed with police gunfire but appears unfazed. Upon noticing the police officer who had been arresting him throughout the film, he fires at him, only to hear a single "click" noise implying his gun is empty. He is killed after the police officer shoots him several times. A repeated clicking noise is heard on the soundtrack implying he was attempting to fire while he was dying.


title: Scarface (1932 film)

text: The first version of the film (Version A) was completed on September 8, 1931, but censors required the ending be modified or they would refuse to grant "Scarface" a license. Paul Muni was unable to re-film the ending in 1931 due to his work on Broadway. Consequently, Hawks was forced to use a body double. The body double was mainly filmed by way of shadows and long shots in order to mask Muni's absence in these scenes. The alternate ending (Version B) differs from the original ending in the manner that Tony is caught and in which he dies. Unlike the original ending, where Tony tries to escape from the police and dies after being shot several times, in the alternate ending, Tony reluctantly hands himself over to the police. After the encounter, Tony's face is not shown. A scene follows where a judge is addressing Tony during sentencing. The next scene is the finale, in which Tony (seen from a bird's eye view) is brought to the gallows and hanged.


title: Scarface (1932 film)

text: However, Version B did not pass the New York censors and Chicago censors. Howard Hughes felt the Hays office had suspicious intentions in rejecting the film because Hays was friends with Louis B. Mayer and Hughes believed censorship was to prevent wealthy independent competitors from producing films. Confident his film could stand out among audiences more than Mayer's films, Hughes organized a press showing of the film in Hollywood and New York. The "New York Herald Tribune" praised Hughes for his courage in opposing the censors. Hughes disowned the censored film and finally in 1932 released Version A with the added text introduction in states that lacked strict censors (Hughes attempted to take the New York censors to court). This 1932 release version led to bonafide box office status and positive critical reviews. Hughes was successful in subsequent lawsuits against the boards that censored the film. Due to criticism from the press, Hays claimed the version shown in theaters was the censored film he had previously approved.


title: Scarface (1932 film)

text: Due to the film's urban setting, nondiegetic music (not visible on the screen or implied to be present in the story) was not used in the film. The only music that appears in the film is during the opening and closing credits and during scenes in the movie where music appears naturally in the film's action such as in the nightclub. Adolf Tandler served as the film's musical director, while Gus Arnheim served as the orchestra's conductor. Gus Arnheim and his Cocoanut Grove Orchestra perform "Saint Louis Blues" by W.C. Handy and "Some of These Days" by Shelton Brooks in the nightclub. The tune Tony whistles in the film is the sextet from Gaetano Donizetti's opera "Lucia di Lammermoor." This tune is accompanied by words that translate to, "What restrains me in such a moment?", and this tune continues to appear during violent scenes in the movie. The song Cesca sings while playing the piano is "Wreck of the Old 97".


title: Scarface (1932 film)

text: The serious play Tony and his friends go to see, leaving at the end of Act 2, is John Colton and Clemence Randolph's "Rain", based on W. Somerset Maugham's story "Miss Sadie Thompson". The play opened on Broadway in 1922 and ran throughout the 1920s. (A film version of the play, also titled "Rain" and starring Joan Crawford, was released by United Artists the same year as "Scarface.") Though fairly inconspicuous in the film, and unnoticed by most viewers, the Camonte family was meant to be partially modeled after the Italo-Spanish Borgia family. This was most prominent through the subtle and arguably incestuous relationship Tony Camonte and his sister share. Camonte's excessive jealousy of his sister's affairs with other men hint at this relationship. Coincidentally, Donizetti wrote the opera for "Lucrezia Borgia", about the Borgia family, and "Lucia di Lammermoor" from where Tony Camonte's whistle tune comes.


title: Scarface (1932 film)

text: After battling with censorship offices, the film was released around a year later than "The Public Enemy" and "Little Caesar". "Scarface" was released in theaters on April 9, 1932. Hughes planned a grand premiere in New York, but New York censor boards rejected the showing of the film. State censorship boards in Ohio, Virginia, Maryland, and Kansas and citywide censorship boards in Detroit, Seattle, Portland, and Chicago banned the film as well. Hughes threatened to sue censorship boards for preventing the release of his film much to the approval of the "New York Herald Tribune". Each state had a different board of censors which allowed Hughes to release the film in areas without strict censorship. At the request of Will Hays, Jason Joy convinced the strict censor boards to allow the release of "Scarface", because the Hays Office acknowledged and appreciated the changes Hughes made to "Scarface". Joy visited state censor boards individually, stating that while the Hays Office was against the positive portrayal of crime, gang films were actually documents against gangster life. Joy was successful and eventually all state and municipal censorship boards allowed "Scarface" to be released, accepting only the cut and censored version of "Scarface".


title: Scarface (1932 film)

text: At the time of release, audiences were generally positive. According to George Raft, who met Al Capone a few times at casinos, even Capone himself liked the film adding, "you tell 'em that if any of my boys are tossin' coins, they'll be twenty-dollar gold pieces." "Variety" cited "Scarface" as having "that powerful and gripping suspense which is in all gangster pictures is in this one in double doses and makes it compelling entertainment," and that the actors play, "as if they'd been doing nothing else all their lives." The National Board of Review named "Scarface" as one of the best pictures of 1932. However, at the time of release in 1932, there was a general public outcry about this motion picture and the gangster genre in general which negatively affected the film's box-office receipts. Jack Alicoate gave "Scarface" a scathing review in "The Film Daily" that the violence and subject matter of the film left him with, "the distinct feeling of nausea". He goes on to say the film "should never have been made" and showing the film would "do more harm to the motion picture industry, and everyone connected with it, than any picture ever shown." Although Ben Hecht was often critical of his work for Hollywood, he admitted that "Scarface" was "the best-directed picture [he has] seen". Hecht did, however, criticize Muni's performance. Having known Al Capone, Hecht claimed that Muni portrayed Capone as too "silent" and "moody", more similar to "Hitler". Some critics disagreed with the casting of British actor Boris Karloff, believing his accent was out of place in a gangster film; a "New York Times" article stated "his British accent is hardly suitable to the role". However, other critics considered him a high point. The film earned $600,000 at the box office and while "Scarface" was more of a financial success than Hughes's other films at the time, due to the large cost of production, it is unlikely the film did better than break even.


title: Scarface (1932 film)

text: The film initiated outrage among Italian organizations and individuals of Italian descent, remarking a tendency of filmmakers to portray gangsters and bootleggers in their films as Italian. In the film, an Italian American makes a speech condemning gangster activities; this was added later in production to appease censors. This, however, did not prevent the Italian embassy from disapproving "Scarface". Believing the film to be offensive to the Italian community, the Order Sons of Italy in America formally denounced the film and other groups urged community members to boycott the film and other films derogatory towards Italians or Italian-Americans. Will Hays wrote to the ambassador in Italy, excusing himself from scrutiny by stating the film was an anachronism because it had been delayed in production for two years and was not representative of the current practice of censorship at the time. Nazi Germany permanently prohibited showings of the film. Some cities in England banned the film as well, believing the British Board of Film Censorship's policy on gangster films was too lax. The film had been banned in Ireland on August 19, 1932 and on August 29, 1941 (under the alternate title of 'Gang War'). The decisions were upheld by the Films Appeal Board each time. It was banned on April 24, 1953 (under its original title). No appeal was lodged. Various reasons include pandering to sensationalism, glamorizing the gangster lifestyle and implying an incestuous relationship between the protagonist and his sister.


title: Scarface (1932 film)

text: Several cities in the United States including Chicago and some states refused to show the film. The magazine "Movie Classics" ran an issue urging the people to demand to see the film at theaters despite the censorship bans. The film broke box-office records at the Woods Theatre in Chicago after premiering Thanksgiving Day, November 20, 1941 after having been banned from showing in Chicago by censors for nine years. Despite the favorable reception of the film among the public, the censorship battles and the unflattering reviews from some press contributed to the film's generally poor performance at the box-office. Upset at the inability to make money from "Scarface", Howard Hughes removed the film from circulation. The film remained unavailable until 1979 except for occasional release prints of suspect quality from questionable sources. Hughes had plans in 1933 to direct and produce a sequel to "Scarface", but due to stricter censorship rules, the film was never made.


title: Scarface (1932 film)

text: Based on a sampling of 46 reviews on Rotten Tomatoes, "Scarface" holds a 98% rating, with an average rating of 8.8/10. The critics' consensus reads: "This "Scarface" foregoes his "little friend" and packs a different kind of heat, blending stylish visuals, thrilling violence, and an incredible cast." It holds a rating of 87 on Metacritic based on 12 reviews, indicating "universal acclaim".


title: Scarface (1932 film)

text: In 1994, "Scarface" was selected for preservation in the United States National Film Registry by the Library of Congress as being "culturally, historically, or aesthetically significant". The character of Tony Camonte ranked at number 47 on "AFI's 100 Years... 100 Heroes and Villains" list. The film was named the best American sound film by critic and director Jean-Luc Godard in "Cahiers du Cinéma". In June 2008, the American Film Institute revealed its "Ten Top Ten"—the best ten films in ten "classic" American film genres—after polling over 1,500 people from the creative community. "Scarface" was acknowledged as the sixth best in the gangster film genre. The 1983 version was placed 10th, making "Scarface" the only film to make the same "10 Top 10" list as its remake.


title: Scarface (1932 film)

text: Scholars debate whether "Scarface" classifies as a film with historical significance or as merely a Hollywood gangster-era motion picture. Its historical significance was augmented by the film's writing credits: W.R. Burnett, author of gangster novel "Little Caesar" from which the film of the same name was based on, Fred D. Pasley, a prominent Chicago gangland historian, and ex-Chicago reporter Ben Hecht. Events similar to the assassination of Jim Colismo and the St. Valentine's Day Massacre contribute to the film's realism and authenticity. Film critic Robert E. Sherwood stated that the film "merits...as a sociological or historical document," and "an utterly inexcusable attempt has been made to suppress it—not because it is obscene...but because...it comes too close to telling the truth."


title: Scarface (1932 film)

text: According to film studies professor Fran Mason, a prominent theme in the film is excess. The opening of the film sets the stage as Big Louie Costillo sits in the remnants of a wild party, convincing his friends his next party will be bigger, better, and have "much more everything". This indicates the excessive life of a gangster, whether in pleasure or in violence. The death scene of Costillo sets the next tone of excess. In this scene, the audience sees only the shadow of Tony Camonte with a gun, hears the shots and the sound of the body hitting the floor. The violent scenes become more severe as the film progresses. Most of the violence in the film is shown through montage, as scenes go by in sequence, showing the brutal murders that Tony and his gang commit such as roughing up bar owners, a drive-by bombing, and the massacre of seven men against a wall. A scene shows a peel-off calendar rapidly changing dates while shot by a machine gun, making the excessive violence clear. The violence is not only perpetrated by the gangsters. The police in the final scene with Tony and Cesca spare no effort to catch the notorious Camonte siblings, visible through the disproportionate number of police officers and cars surrounding the apartment complex to apprehend one man. Tony and the police's excessive use of violence throughout the film normalizes it. An element of parody underlies Tony's abnormal joy in using Tommy guns. In the scene in the restaurant in which men from the North Side gang attempt to shoot Tony with a Tommy, he obtains pleasure from the power. Rather than cowering beneath the tables, he tries to peek out to watch the guns in action, laughing maniacally from his excitement. He reacts jovially upon getting his first Tommy gun and enthusiastically leaves to, "write [his] name all over the town with it in big letters."


title: Scarface (1932 film)

text: The gangster's excessive consumption is comically represented through Tony's quest to obtain expensive goods and show them off. In Tony's first encounter with Poppy alone on the staircase, he boasts about his new suit, jewelry, and bullet-proof car. Poppy largely dismisses his advances calling his look, "kinda effeminate". His feminine consumption and obsession with looks and clothes is juxtaposed by his masculine consumption which is represented by his new car. Later, Tony shows Poppy a stack of new shirts, claiming he will wear each shirt only once. His awkwardness and ignorance of his own exorbitance make this Gatsby style scene more comical than serious. His consumption serves to symbolize the disintegration of values of modernity, specifically represented by his poor taste and obsession with money and social status. Tony's excess transcends parody and becomes dangerous because he represents a complete lack of restraint which ultimately leads to his downfall.


title: Scarface (1932 film)

text: Tony's excess is manifested in the gang wars in the city. He is given express instruction to leave O'Hara, Gaffney, and the rest of the North Side gang alone. He disobeys because of his lust for more power, violence, and territory. Not only does he threaten the external power structure of the gangs in relation to physical territory, but he also disrupts the internal power structure of his own gang by blatantly disobeying his boss Johnny Lovo. Gaffney's physical position juxtaposes Tony's position. Throughout the film, Gaffney's movement is restricted by both setting and implication, because of the crowded spaces in which he is shown onscreen and his troupe of henchmen he is constantly surrounded by. Tony is able to move freely at the beginning of the film, becoming progressively more crowded until he is as confined as Gaffney. He is surrounded by henchmen and cannot move as freely throughout the city. This, however, is self-imposed by his own excessive desire for territory and power.


title: Scarface (1932 film)

text: The theme of excessiveness is further exemplified by Tony's incestuous desires for his sister, Cesca, whom he attempts to control and restrict. Their mother acts as the voice of reason, but Tony does not listen to her, subjecting his family to the excess and violence he brings upon himself. His lust for violence mirror's Cesca's lust for sexual freedom, symbolized by her seductive dance for Rinaldo at the club. Rinaldo is split between his loyalty for Tony and his passion for Cesca, serving as a symbol of the power struggle between the Camonte siblings. Rinaldo is a symbol of Tony's power and prominence; his murder signifies Tony's lack of control and downfall, which ends in Tony's own death.