In this task, you are given a context, a subject, a relation, and many options. Based on the context, from the options select the object entity that has the given relation with the subject. Answer with text (not indexes).

[EX Q]: Context: South Cotabato, officially the Province of South Cotabato (Maguindanaon: "Kuta Wato Saut"), is a province in the Philippines located in the SOCCSKSARGEN region in Mindanao. Its capital is Koronadal City, and it borders Sultan Kudarat to the north and west, Sarangani to the south and northeast, and Davao del Sur to the far northeast. To the southeast lies Sarangani Bay., Taiwan, officially the Republic of China (ROC), is a state in East Asia. Neighbors include China (officially the People's Republic of China, abbreviated as PRC) to the west, Japan to the northeast, and the Philippines to the south.
Taiwan is the most populous state that is not a member of the United Nations, and the one with the largest economy., Davao del Sur is a province in the Philippines located in the Davao Region in Mindanao. Its capital and largest city is Digos. The province is bordered by Davao City to the north, Davao Occidental to the south and Cotabato, Sultan Kudarat, South Cotabato and Sarangani to the west. To the east lies the Davao Gulf., Sarangani Bay is a bay located on the southern tip of Mindanao in the Philippines. It opens up to the Celebes Sea on the Pacific Ocean. General Santos City, one of the Philippines most important cities and ports, is located at the head of the bay, making the bay one of the busiest and often the sight of shipping accidents. The province of Sarangani, created in 1992, is named after the bay., Palau (historically Belau or Pelew), officially the Republic of Palau, is an island country located in the western Pacific Ocean. The country contains approximately 250 islands, forming the western chain of the Caroline Islands in Micronesia, and has an area of . The most populous island is Koror. The capital Ngerulmud is located on the nearby island of Babeldaob, in Melekeok State. Palau shares maritime boundaries with Indonesia, the Philippines, and the Federated States of Micronesia., Metropolitan Manila, commonly known as Metro Manila or simply Manila, is the capital region of the Philippines, is the seat of government, the 2nd most populous and the most densely populated region of the country. The National Capital Region (NCR) is composed of Manila, the capital city of the country, Quezon City, the country's most populous city, and the cities of Caloocan, Las Piñas, Makati, Malabon, Mandaluyong, Marikina, Muntinlupa, Navotas, Parañaque, Pasay, Pasig, San Juan, Taguig, and Valenzuela, including the only remaining municipality of Pateros., Luzon is the largest and most populous island in the Philippines and the 15th largest in the world. Located in the northern region of the archipelago, it is the economic and political center of the nation, being home to the country's capital city, Manila, as well as Quezon City, the country's most populous. With a population of 52.99 million , it is the fourth most populous island in the world (after Java, Honshu, and Great Britain), containing about 53% of the country's total population., The Celebes Sea of the western Pacific Ocean is bordered on the north by the Sulu Archipelago and Sulu Sea and Mindanao Island of the Philippines, on the east by the Sangihe Islands chain, on the south by Sulawesi's Minahassa Peninsula, and on the west by Kalimantan in Indonesia. It extends 420 miles (675 km) north-south by 520 miles (837 km) east-west and has a total surface area of , to a maximum depth of . The sea opens southwest through the Makassar Strait into the Java Sea., Malapatan is a first class municipality in the province of Sarangani , Philippines . According to the 2010 census , it has a population of 72,386 people . As of 2010 , it has a total voting population of 35,569 voters . Malapatan is bounded on the west by Sarangani Bay , on the east by Davao del Sur , on the north by Alabel , and on the south by Glan ., Asia is Earth's largest and most populous continent, located primarily in the eastern and northern hemispheres and sharing the continental landmass of Eurasia with the continent of Europe. Asia covers an area of , about 30% of Earth's total land area and 8.7% of the Earth's total surface area. The continent, which has long been home to the majority of the human population, was the site of many of the first civilizations. Asia is notable for not only its overall large size and population, but also dense and large settlements as well as vast barely populated regions within the continent of 4.4 billion people., The Philippine Sea is a marginal sea east and northeast of the Philippines occupying an estimated surface area of 5 million km² (2 million mi²). of the western part of the North Pacific Ocean. It is bordered by the Philippine archipelago (Luzon, Catanduanes, Samar, Leyte and Mindanao) on the southwest; Halmahera, Morotai, Palau, Yap, and Ulithi (of the Carolines) on the southeast; the Marianas, including Guam, Saipan, and Tinian, on the east; the Bonin and Iwo Jima on the northeast; the Japanese islands of Honshu, Shikoku, and Kysh on the north; the Ryukyu Islands on the northwest; and Taiwan in the west., An island country is a country whose primary territory consists of one or more islands or parts of islands. As of 2011, 46 (approximately 24%) of the 193 UN member states are island countries., Southeast Asia or Southeastern Asia is a subregion of Asia, consisting of the countries that are geographically south of China, east of India, west of New Guinea and north of Australia. The region lies near the intersection of geological plates, with heavy seismic and volcanic activity. Southeast Asia consists of two geographic regions:, Vietnam, officially the Socialist Republic of Vietnam (SRV), is the easternmost country on the Indochina Peninsula in Southeast Asia. With an estimated 90.5 million inhabitants , it is the world's 14th-most-populous country, and the eighth-most-populous Asian country. Vietnam is bordered by China to the north, Laos to the northwest, Cambodia to the southwest, Thailand across the Gulf of Thailand to the southwest, and the Philippines, Malaysia and Indonesia across the South China Sea to the east and southeast. Its capital city has been Hanoi since the reunification of North and South Vietnam in 1976., The Philippines, officially the Republic of the Philippines, is a sovereign island country in Southeast Asia situated in the western Pacific Ocean. It consists of about 7,641 islands that are categorized broadly under three main geographical divisions from north to south: Luzon, Visayas, and Mindanao. The capital city of the Philippines is Manila and the most populous city is Quezon City, both part of Metro Manila. Bounded by the South China Sea on the west, the Philippine Sea on the east and the Celebes Sea on the southwest, the Philippines shares maritime borders with Taiwan to the north, Vietnam to the west, Palau to the east and Malaysia and Indonesia to the south., Indonesia (or ; Indonesian: ), officially the Republic of Indonesia, is a unitary sovereign state and transcontinental country located mainly in Southeast Asia with some territories in Oceania. Situated between the Indian and Pacific oceans, it is the world's largest island country, with more than seventeen thousand islands. At , Indonesia is the world's 14th-largest country in terms of land area and world's 7th-largest country in terms of combined sea and land area. It has an estimated population of over 260 million people and is the world's fourth most populous country, the most populous Austronesian nation, as well as the most populous Muslim-majority country. The world's most populous island of Java contains more than half of the country's population., Soccsksargen (officially styled as SOCCSKSARGEN) (pronounced ) is an administrative region of the Philippines, located in south-central Mindanao. It is numerically designated as Region XII. The name is an acronym that stands for the region's four provinces (South Cotabato, Cotabato, Sultan Kudarat and Sarangani) and one of its cities (General Santos). The region used to be called "Central Mindanao". The regional center is Koronadal located in the province of South Cotabato, and the center of commerce, industry and the most populous city is General Santos., China, officially the People's Republic of China (PRC), is a unitary sovereign state in East Asia. With a population of over 1.381 billion, it is the world's most populous country. The state is governed by the Communist Party of China, and its capital is Beijing. It exercises jurisdiction over 22 provinces, five autonomous regions, four direct-controlled municipalities (Beijing, Tianjin, Shanghai, and Chongqing), and two mostly self-governing special administrative regions (Hong Kong and Macau), and claims sovereignty over Taiwan. The country's major urban areas include Shanghai, Guangzhou, Beijing, Chongqing, Shenzhen, Tianjin and Hong Kong. China is a great power and a major regional power within Asia, and has been characterized as a potential superpower., Malaysia is a federal constitutional monarchy located in Southeast Asia. It consists of thirteen states and three federal territories and has a total landmass of separated by the South China Sea into two similarly sized regions, Peninsular Malaysia and East Malaysia (Malaysian Borneo). Peninsular Malaysia shares a land and maritime border with Thailand and maritime borders with Singapore, Vietnam, and Indonesia. East Malaysia shares land and maritime borders with Brunei and Indonesia and a maritime border with the Philippines and Vietnam. The capital city is Kuala Lumpur, while Putrajaya is the seat of the federal government. With a population of over 30 million, Malaysia is the 44th most populous country. The southernmost point of continental Eurasia, Tanjung Piai, is in Malaysia. Located in the tropics, Malaysia is one of 17 megadiverse countries on earth, with large numbers of endemic species., Sarangani, or "Saragani", is a province in the Philippines located in the Soccsksargen region. Its capital is Alabel. With a coastline along the Sarangani Bay and Celebes Sea, the province is at the southernmost tip of Mindanao island, and borders South Cotabato and Davao del Sur to the north, Davao Occidental to the east, and the Celebes Sea to the south., Manila (or ), officially City of Manila, is the capital of the Philippines., Mindanao is the second largest and southernmost major island in the Philippines. It is also the name of one of the three island groups in the country (the other two being Luzon and the Visayas), consisting of the island of Mindanao and smaller outlying islands. Davao City is the largest city in Mindanao. As of the 2010 census, the island's population itself is 20,281,545 people, while the Mindanao island group has 21,968,174 inhabitants. Davao City is the most populous in Mindanao as 1,632,991 population, and the 2nd is Zamboanga City as 861,799 population, the 3rd is Cagayan de Oro City as 675,950 population, and followed by General Santos City as 594,446 population as of 2015 census., Quezon City (  also known as QC) is the most populous city in the Philippines. It is one of the cities that make up Metro Manila, the National Capital Region of the Philippines. Quezon City was named after Manuel L. Quezon, second President of the Philippines, who founded the city and developed it to replace Manila as the national capital for 28 years from 1948 to 1976. Quezon City is not located in and should not be confused with Quezon Province, which was also named after the president. It is the largest city in Metro Manila in terms of land area and most populated local government unit in the country., The South China Sea is a marginal sea that is part of the Pacific Ocean, encompassing an area from the Karimata and Malacca Straits to the Strait of Taiwan of around . The area's importance largely results from one-third of the world's shipping sailing through its waters and that it is believed to hold huge oil and gas reserves beneath its seabed., The Visayas or the Visayan Islands (Visayan: "Kabisay-an",  ), is one of the three principal geographical divisions of the Philippines, along with Luzon and Mindanao. It consists of several islands, primarily surrounding the Visayan Sea, although the Visayas are considered the northeast extremity of the entire Sulu Sea. Its inhabitants are predominantly the Visayan people., Subject: malapatan, Relation: shares_border_with, Options: (A) as (B) asia (C) cagayan de oro (D) celebes sea (E) chongqing (F) davao city (G) davao del sur (H) digos (I) east (J) general santos (K) guangzhou (L) hong kong (M) indonesia (N) island (O) java sea (P) leyte (Q) major (R) malaysia (S) manila (T) most (U) muntinlupa (V) national capital region (W) navotas (X) north (Y) northern region (Z) northwest ([) pacific ocean (\) palau (]) parañaque (^) pasig (_) putrajaya (`) quezon (a) quezon city (b) sarangani (c) shanghai (d) south (e) southwest (f) sulu sea (g) sur (h) taiwan (i) tianjin (j) valenzuela (k) vietnam
[EX A]: general santos

[EX Q]: Context: The biological family Canidae  The cat-like feliforms and dog-like caniforms emerged within the Carnivoramorpha 43 million years before present. The caniforms included the fox-like "Leptocyon" genus whose various species existed from 34 million years before present before branching 11.9 million YBP into Vulpini (foxes) and Canini (canines).  Canids are found on all continents except Antarctica, having arrived independently or accompanied human beings over extended periods of time. Canids vary in size from the 2-m-long (6 ft 7 in) gray wolf to the 24-cm-long (9.4 in) fennec fox. The body forms of canids are similar, typically having long muzzles, upright ears, teeth adapted for cracking bones and slicing flesh, long legs, and bushy tails. They are mostly social animals, living together in family units or small groups and behaving cooperatively. Typically, only the dominant pair in a group breeds, and a litter of young is reared annually in an underground den. Canids communicate by scent signals and by vocalizations. They are very intelligent. One canid, the domestic dog, long ago entered into a partnership with humans and today remains one of the most widely kept domestic animals., Roman Stanisaw Dmowski (9 August 1864  2 January 1939) was a Polish politician, statesman, and co-founder and chief ideologue of the right-wing National Democracy ("ND": in Polish, ""Endecja"") political movement. He saw the aggressive Germanization of Polish territories controlled by the German Empire as the major threat to Polish culture and therefore advocated a degree of accommodation with another power that had partitioned Poland, the Russian Empire. He favored the re-establishment of Polish independence by nonviolent means, and supported policies favorable to the Polish middle class. During World War I, in Paris, through his Polish National Committee he was a prominent spokesman, to the Allies, for Polish aspirations. He was a principal figure instrumental in the postwar restoration of Poland's independent existence., National Democracy (also known from its abbreviation ND as "Endecja") was a Polish political movement active from the second half of the 19th century under the foreign partitions of the country until the end of the Second Polish Republic.<ref name="Szukaa/Hall"></ref> It ceased to exist after the Nazi-Soviet invasion of Poland of 1939. In its long history, National Democracy went through several stages of development. Created with the intention of promoting the fight for Poland's sovereignty against the repressive imperial regimes, the movement acquired its right-wing nationalist character following the return to independence. A founder and principal ideologue was Roman Dmowski. Other ideological fathers of the movement included Zygmunt Balicki and Jan Ludwik Popawski., League and Self - Defense ( Polish : Liga i Samoobrona , LiS -- lis also means fox in Polish ) was the proposed name for a new Polish political grouping which was to arise from an alliance or merger between the left - wing populist Self - Defense of the Republic of Poland ( SORP ) and the national conservative Christian right League of Polish Families ( LPR ) in July 2007 . However , the merger failed to materialise , and LiS did n't go anywhere beyond the stage of a proposal . The decision for the synthesis of the two parties arose following a crisis within Poland 's ruling three party coalition , of the dominant Law and Justice ( PiS ) party , and junior partners SORP and LPR . On 9 July , SORP leader , Andrzej Lepper , was dismissed from his position as Minister for Agriculture following a secret investigation by the Central Anticorruption Bureau ( CBA ) which attempted to link him and his department to corruptive practices . Lepper protested his innocence and claimed to have been the victim of a politically motivated ' sting ' operation , initiated by PM Kaczynski and PiS . He demanded that a parliamentary inquiry be conducted to investigate the legality and motivation of the CBA operation mounted against him . Lepper 's stance drew him support from his own SORP party and the LPR . On 16 July 2007 , a merger of the two parties was announced at a press conference conducted by Lepper and his LPR counterpart , Roman Giertych . The nature of this new ' LiS ' was not made clear , and the leaders could not give any specifics as to whether LiS would take the form of a newly unified party or simply an electoral alliance of two autonomous parties . It was indicated however , that the platform of this new alliance would be mainly eurosceptic and anti-reformist . By early September it was clear that LiS would not arise . The membership of the two parties had not been properly consulted as to their support for this idea , and the merits of the proposition had not been discussed . Many of the members of both groups saw little common ground between the two parties . Furthermore , opinion polls did not necessarily reflect that there was a significant advantage to an alliance . LPR and SORP therefore decided to start independently of each other at the early 21 October legislative elections . LPR joined forces with Real Politics Union and Right of the Republic to form a new alliance called League of the Right of the Republic ( Liga Prawicy Rzeczypospolitej ) ., Mammals are any vertebrates within the class Mammalia (from Latin "mamma" "breast"), a clade of endothermic amniotes distinguished from reptiles and birds by the possession of a neocortex (a region of the brain), hair, three middle ear bones and mammary glands. The sister group of mammals may be the extinct "Haldanodon." The mammals represent the only living Synapsida, which together with the Sauropsida form the Amniota clade. The mammals consist of the Yinotheria including monotrema and the Theriiformes including the theria., The tail is the section at the rear end of an animal's body; in general, the term refers to a distinct, flexible appendage to the torso. It is the part of the body that corresponds roughly to the sacrum and coccyx in mammals, reptiles, and birds. While tails are primarily a feature of vertebrates, some invertebrates including scorpions and springtails, as well as snails and slugs, have tail-like appendages that are sometimes referred to as tails. Tailed objects are sometimes referred to as "caudate" and the part of the body associated with or proximal to the tail are given the adjective "caudal"., The domestic dog ("Canis lupus familiaris" or "Canis familiaris") is a member of genus "Canis" (canines) that forms part of the wolf-like canids, and is the most widely abundant carnivore. The dog and the extant gray wolf are sister taxa, with modern wolves not closely related to the wolves that were first domesticated. The dog was the first domesticated species and has been selectively bred over millennia for various behaviors, sensory capabilities, and physical attributes., Foxes are small-to-medium-sized, omnivorous mammals belonging to several genera of the family Canidae. Foxes are slightly smaller than a medium-size domestic dog, with a flattened skull, upright triangular ears, a pointed, slightly upturned snout, and a long bushy tail (or "brush")., A snout is the protruding portion of an animal's face, consisting of its nose, mouth, and jaw. In many animals the equivalent structure is called a muzzle, rostrum or proboscis. The wet, naked surface around the nostrils of the nose of some animals is known as the rhinarium (colloquially this is the "cold wet nose" of some animals). The rhinarium is often associated with a stronger sense of olfaction. The snout is considered a weak point on most animals: because of its structure, an animal can be easily stunned, snapped or even knocked out by applying sufficient force., Poland, officially the Republic of Poland, is a country in Central Europe, situated between the Baltic Sea in the north and two mountain ranges (the Sudetes and Carpathian Mountains) in the south. Bordered by Germany to the west; the Czech Republic and Slovakia to the south; Ukraine and Belarus to the east; and the Baltic Sea, Kaliningrad Oblast (a Russian exclave) and Lithuania to the north. The total area of Poland is , making it the 69th largest country in the world and the 9th largest in Europe. With a population of over 38.5 million people, Poland is the 34th most populous country in the world, the 8th most populous country in Europe and the sixth most populous member of the European Union. Poland is a unitary state divided into 16 administrative subdivisions, and its capital and largest city is Warsaw. Other metropolises include Kraków, Wrocaw, Pozna, Gdask and Szczecin., Roman Jacek Giertych (born 27 February 1971 in rem, Poland) is a Polish politician; he was Deputy Prime Minister and Minister of Education until August 2007. He was a member of the Sejm (the lower house of the Polish parliament) from 2001 until October 2007 and the chairman of the League of Polish Families party., Christian right or religious right is a term used mainly in the United States to label right-wing Christian political factions that are characterized by their strong support of socially conservative policies. Christian conservatives principally seek to apply their understanding of the teachings of Christianity to politics and to public policy by proclaiming the value of those teachings or by seeking to use those teachings to influence law and public policy., The League of Polish Families (Polish: "Liga Polskich Rodzin", LPR) is a nationalist conservative political party in Poland, part of the Catholic-National Movement and with many elements of far-right ideology. The party's original ideology was that of the national democracy movement which was headed by Roman Dmowski, however in 2006 its leader Roman Giertych distanced himself from that heritage., Subject: league and self-defense, Relation: instance_of, Options: (A) adjective (B) animal (C) august (D) brain (E) cat (F) century (G) christian (H) city (I) clade (J) class (K) committee (L) country (M) culture (N) democracy (O) dog (P) education (Q) empire (R) exclave (S) family (T) feature (U) february (V) fox (W) genus (X) gray wolf (Y) group (Z) hall ([) human (\) humans (]) ideology (^) instrumental (_) invasion (`) label (a) league (b) member (c) minister (d) mountain (e) name (f) part (g) point (h) political movement (i) political party (j) politics (k) population (l) public (m) region (n) republic (o) restoration (p) saw (q) sense (r) size (s) soviet (t) structure (u) surface (v) term (w) three (x) understanding (y) union (z) war ({) wing (|) world war
[EX A]: political party

[EX Q]: Context: Daniel E. Gorenstein ( January 1 , 1923 -- August 26 , 1992 ) was an American mathematician . He earned his undergraduate and graduate degrees at Harvard University , where he earned his Ph.D. in 1950 under Oscar Zariski , introducing in his dissertation a duality principle for plane curves that motivated Grothendieck 's introduction of Gorenstein rings . He was a major influence on the classification of finite simple groups . After teaching mathematics to military personnel at Harvard before earning his doctorate , Gorenstein held posts at Clark University and Northeastern University before he began teaching at Rutgers University in 1969 , where he remained for the rest of his life . He was the founding director of DIMACS in 1989 , and remained as its director until his death . Gorenstein was awarded many honors for his work on finite simple groups . He was recognised , in addition to his own research contributions such as work on signalizer functors , as a leader in directing the classification proof , the largest collaborative piece of pure mathematics ever attempted . In 1972 he was a Guggenheim Fellow and a Fulbright Scholar ; in 1978 he gained membership in the National Academy of Sciences and the American Academy of Arts and Sciences , and in 1989 won the Steele Prize for mathematical exposition ., A research university is a university that expects all its tenured and tenure-track faculty to continuously engage in research, as opposed to merely requiring it as a condition of an initial appointment or tenure. Such universities can be recognized by their strong focus on innovative research and the prestige of their brand names. On the one hand, research universities strive to recruit faculty who are the most brilliant minds in their disciplines in the world, and their students enjoy the opportunity to learn from such experts. On the other hand, new students are often disappointed to realize their undergraduate courses at research universities are overly academic and fail to provide vocational training with immediate "real world" applications; but many employers value degrees from research universities because they know that such coursework develops fundamental skills like critical thinking. , Harvard University is a private Ivy League research university in Cambridge, Massachusetts, established in 1636, whose history, influence, and wealth have made it one of the world's most prestigious universities., The Ivy League is a collegiate athletic conference comprising sports teams from eight private institutions of higher education in the Northeastern United States. The conference name is also commonly used to refer to those eight schools as a group beyond the sports context. The eight institutions are Brown University, Columbia University, Cornell University, Dartmouth College, Harvard University, the University of Pennsylvania, Princeton University, and Yale University. The term "Ivy League" has connotations of academic excellence, selectivity in admissions, and social elitism., Russia (from the  Rus'), also officially known as the Russian Federation, is a country in Eurasia. At , Russia is the largest country in the world by surface area, covering more than one-eighth of the Earth's inhabited land area, and the ninth most populous, with over 140 million people at the end of March 2016. The European western part of the country is much more populated and urbanised than the eastern, about 77% of the population live in European Russia. Russia's capital Moscow is one of the largest cities in the world, other major urban centers include Saint Petersburg, Novosibirsk, Yekaterinburg, Nizhny Novgorod and Samara., In number theory, integer factorization is the decomposition of a composite number into a product of smaller integers. If these integers are further restricted to prime numbers, the process is called prime factorization., A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number. For example, 5 is prime because 1 and 5 are its only positive integer factors, whereas 6 is composite because it has the divisors 2 and 3 in addition to 1 and 6. The fundamental theorem of arithmetic establishes the central role of primes in number theory: any integer greater than 1 can be expressed as a product of primes that is unique up to ordering. The uniqueness in this theorem requires excluding 1 as a prime because one can include arbitrarily many instances of 1 in any factorization, e.g., 3, 1 · 3, 1 · 1 · 3, etc. are all valid factorizations of 3., Cambridge is a city in Middlesex County, Massachusetts, United States, in the Boston metropolitan area., A mathematical problem is a problem that is amenable to being represented, analyzed, and possibly solved, with the methods of mathematics. This can be a real-world problem, such as computing the orbits of the planets in the solar system, or a problem of a more abstract nature, such as Hilbert's problems.<br>
It can also be a problem referring to the nature of mathematics itself, such as Russell's Paradox., In mathematics, the classification of the finite simple groups is a theorem stating that every finite simple group belongs to one of four broad classes described below. These groups can be seen as the basic building blocks of all finite groups, in a way reminiscent of the way the prime numbers are the basic building blocks of the natural numbers. The JordanHölder theorem is a more precise way of stating this fact about finite groups. However, a significant difference with respect to the case of integer factorization is that such "building blocks" do not necessarily determine uniquely a group, since there might be many non-isomorphic groups with the same composition series or, put in another way, the extension problem does not have a unique solution., Mathematics (from Greek  "máthma", knowledge, study, learning) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics., In abstract algebra, a finite group is a mathematical group with a finite number of elements. A group is a set of elements together with an operation which associates, to each ordered pair of elements, an element of the set. With a finite group, the set is finite. , Oscar Zariski (born Oscher Zaritsky (April 24, 1899  July 4, 1986) was a Russian-born American mathematician and one of the most influential algebraic geometers of the 20th century., In abstract algebra, a composition series provides a way to break up an algebraic structure, such as a group or a module, into simple pieces. The need for considering composition series in the context of modules arises from the fact that many naturally occurring modules are not semisimple, hence cannot be decomposed into a direct sum of simple modules. A composition series of a module "M" is a finite increasing filtration of "M" by submodules such that the successive quotients are simple and serves as a replacement of the direct sum decomposition of "M" into its simple constituents. , A mathematician is someone who uses an extensive knowledge of mathematics in his/her work, typically to solve mathematical problems., Subject: daniel gorenstein, Relation: place_of_birth, Options: (A) boston (B) cambridge (C) harvard (D) hilbert (E) jordan (F) march (G) massachusetts (H) middlesex county (I) moscow (J) most (K) nizhny novgorod (L) of (M) pennsylvania (N) petersburg (O) russia (P) saint petersburg (Q) strong (R) yekaterinburg
[EX A]:
boston