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).
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Question: Context: Colombia (or ), officially the Republic of Colombia, is a transcontinental country largely situated in the northwest of South America, with territories in Central America. Colombia shares a border to the northwest with Panama, to the east with Venezuela and Brazil and to the south with Ecuador and Peru. It shares its maritime limits with Costa Rica, Nicaragua, Honduras, Jamaica, the Dominican Republic and Haiti. It is a unitary, constitutional republic comprising thirty-two departments. The territory of what is now Colombia was originally inhabited by indigenous peoples including the Muisca, the Quimbaya and the Tairona., A mathematician is someone who uses an extensive knowledge of mathematics in his/her work, typically to solve mathematical problems., An astronomer is a scientist in the field of astronomy who concentrates their studies on a specific question or field outside of the scope of Earth. They look at stars, planets, moons, comets and galaxies, as well as many other celestial objects  either in observational astronomy, in analyzing the data or in theoretical astronomy. Examples of topics or fields astronomers work on include: planetary science, solar astronomy, the origin or evolution of stars, or the formation of galaxies. There are also related but distinct subjects like physical cosmology which studies the Universe as a whole., Pedro Vicente Maldonado is a canton in the west of the province of Pichincha in Ecuador . It is named after the 18th - century Ecuadoran scientist Pedro Vicente Maldonado . Arashá Spa , a tropical forest resort , is located in this canton ., The Equator usually refers to an imaginary line on the Earth's surface equidistant from the North Pole and South Pole, dividing the Earth into the Northern Hemisphere and Southern Hemisphere. The Equator is about long; some 78.7% lies across water and 21.3% over land., Quito, formally San Francisco de Quito, is the capital city of Ecuador, and at an elevation of above sea level, it is the highest official capital city in the world and the one which is closest to the equator. It is located in the Guayllabamba river basin, on the eastern slopes of Pichincha, an active stratovolcano in the Andes mountains. With a population of 2,671,191 according to the last census (2014), Quito is the second most populous city in Ecuador, after Guayaquil. It is also the capital of the Pichincha province and the seat of the Metropolitan District of Quito. The canton recorded a population of 2,239,191 residents in the 2010 national census. In 2008, the city was designated as the headquarters of the Union of South American Nations., Peru , officially the Republic of Peru, is a country in western South America. It is bordered in the north by Ecuador and Colombia, in the east by Brazil, in the southeast by Bolivia, in the south by Chile, and in the west by the Pacific Ocean. Peru is an extremely biodiverse country with habitats ranging from the arid plains of the Pacific coastal region in the west to the peaks of the Andes mountains vertically extending from the north to the southeast of the country to the tropical Amazon Basin rainforest in the east with the Amazon river., London is the capital and most populous city of England and the United Kingdom, as well as the most populous city proper in the European Union. Standing on the River Thames in the south east of the island of Great Britain, London has been a major settlement for two millennia. It was founded by the Romans, who named it "Londinium". London's ancient core, the City of London, largely retains its medieval boundaries. Since at least the 19th century, "London" has also referred to the metropolis around this core, historically split between Middlesex, Essex, Surrey, Kent, and Hertfordshire, which today largely makes up Greater London, governed by the Mayor of London and the London Assembly., Pedro Vicente Maldonado y Flores, (Riobamba, Royal Audience of Quito (today's Ecuador) November 24, 1704  London, England, November 17, 1748) was a South-American scientist who collaborated with the members of the French Geodesic Mission. As well as a physicist and a mathematician, Maldonado was an astronomer, topographer, and geographer., Ecuador, officially the Republic of Ecuador (which literally translates as "Republic of the Equator"), is a representative democratic republic in northwestern South America, bordered by Colombia on the north, Peru on the east and south, and the Pacific Ocean to the west. Ecuador also includes the Galápagos Islands in the Pacific, about west of the mainland.,  There are three ma"jor fields of study, which are further subdivided:" The National Geographic Society identifies five broad key themes for geographers:, Riobamba (full name San Pedro de Riobamba) is the capital of the Chimborazo Province in central Ecuador, which is located at the Chambo River Valley of the Andes. It is south of Ecuador's capital Quito and located at 2754 m on the Avenue of the Volcanoes. The city is an important regional transport center as well as being a stop on the Pan-American Highway that runs through Ecuador. Riobamba stands as one of the largest cities in the central portion of Ecuador's Sierra region., South America is a continent located in the western hemisphere, mostly in the southern hemisphere, with a relatively small portion in the northern hemisphere. It is also considered a subcontinent of the Americas, which is the model used in nations that speak Romance languages. The reference to South America instead of other regions (like Latin America or the Southern Cone) has increased in the last decades due to changing geopolitical dynamics (in particular, the rise of Brazil)., The Pacific Ocean is the largest of the Earth's oceanic divisions. It extends from the Arctic Ocean in the north to the Southern Ocean (or, depending on definition, to Antarctica) in the south and is bounded by Asia and Australia in the west and the Americas in the east., The Galápagos Islands (official name: "Archipiélago de Colón", other Spanish name: "Islas Galápagos") are an archipelago of volcanic islands distributed on either side of the Equator in the Pacific Ocean surrounding the centre of the Western Hemisphere, west of continental Ecuador, of which they are a part. The islands are known for their vast number of endemic species and were studied by Charles Darwin during the voyage of the "Beagle", as his observations and collections contributed to the inception of Darwin's theory of evolution by natural selection., The French Geodesic Mission (also called the Geodesic Mission to Peru, Geodesic Mission to the Equator and the Spanish-French Geodesic Mission) was an 18th-century expedition to what is now Ecuador carried out for the purpose of measuring the roundness of the Earth and measuring the length of a degree of latitude at the Equator. The mission was one of the first geodesic (or "geodetic") missions carried out under modern scientific principles, and the first major international scientific expedition., England is a country that is part of the United Kingdom. It shares land borders with Scotland to the north and Wales to the west. The Irish Sea lies northwest of England and the Celtic Sea lies to the southwest. England is separated from continental Europe by the North Sea to the east and the English Channel to the south. The country covers five-eighths of the island of Great Britain (which lies in the North Atlantic) in its centre and south; and includes over 100 smaller islands such as the Isles of Scilly, and the Isle of Wight., A physicist is a scientist who has specialized knowledge in the field of physics, the exploration of the interactions of matter and energy across the physical universe., Subject: pedro vicente maldonado canton, Relation: located_in_the_administrative_territorial_entity, Options: (A) antarctica (B) basin (C) canton (D) center (E) central (F) centre (G) chimborazo province (H) city of london (I) colombia (J) costa rica (K) darwin (L) earth (M) east (N) ecuador (O) england (P) europe (Q) flores (R) galápagos islands (S) haiti (T) hertfordshire (U) jamaica (V) london (W) maldonado (X) mission (Y) north (Z) northwest ([) of (\) pacific ocean (]) panama (^) peru (_) pichincha province (`) quito (a) riobamba (b) river (c) scotland (d) south (e) southwest (f) surrey (g) venezuela

Answer: pichincha province


Question: Context: Liquidizer is the debut album by British rock band Jesus Jones , released in 1989 on SBK Records . Single releases were `` Info Freako '' , `` Never Enough '' and `` Bring It On Down '' ., Alternative rock (also called alternative music, alt-rock or simply alternative) is a genre of rock music that emerged from the independent music underground of the 1980s and became widely popular in the 1990s and 2000s. In this instance, the word "alternative" refers to the genre's distinction from mainstream rock music. The term's original meaning was broader, referring to a generation of musicians unified by their collective debt to either the musical style or simply the independent, D.I.Y. ethos of punk rock, which in the late 1970s laid the groundwork for alternative music. At times, "alternative" has been used as a catch-all description for music from underground rock artists that receives mainstream recognition, or for any music, whether rock or not, that is seen to be descended from punk rock (including some examples of punk itself, as well as new wave, and post-punk)., Wiltshire (or ) is a county in South West England with an area of . It is landlocked and borders the counties of Dorset, Somerset, Hampshire, Gloucestershire, Oxfordshire and Berkshire. The county town was Wilton but Wiltshire Council is now based in the new county town of Trowbridge., Jesus Jones are a British alternative rock band from Bradford-on-Avon in Wiltshire, formed in late 1988, recorded and performed in the late 1980s into the 2000s. Their track "Right Here, Right Now" was an international hit which was subsequently globally licensed for promotional and advertising campaigns. They also achieved chart success with the songs "Real Real Real," "International Bright Young Thing" and "Info Freako"., "Real Real Real" is a song from the UK band Jesus Jones' 1991 album "Doubt". It was released in 1990 as the first single from "Doubt", just prior to the release of the album. It was succeeded by the "Billboard" Top 10 hit "Right Here, Right Now" (which, in the UK peaked at No. 31). "Real Real Real" did better, reaching a peak of No. 19 on the UK Singles Chart. It was also their second Top 10 US hit, peaking at No. 4 on the "Billboard" Hot 100. The song is featured on the "Happy Daze" compilation., Subject: liquidizer , Relation: followed_by, Options: (A) 10 (B) 100 (C) 19 (D) 1980s (E) 1988 (F) 31 (G) 4 (H) a (I) album (J) alternative (K) as (L) be (M) bright (N) catch (O) collective (P) compilation (Q) d (R) doubt (S) first (T) here (U) international (V) is (W) jesus (X) mainstream (Y) music (Z) new ([) new wave (\) no (]) no . 4 (^) or (_) popular (`) post (a) real (b) release (c) right here , right now (d) rock (e) south (f) style (g) the album (h) they (i) this (j) to be (k) underground (l) wave (m) west (n) y (o) young

Answer: doubt


Question: Context: Commutative algebra is the branch of algebra that studies commutative rings, their ideals, and modules over such rings. Both algebraic geometry and algebraic number theory build on commutative algebra. Prominent examples of commutative rings include polynomial rings, rings of algebraic integers, including the ordinary integers formula_1, and "p"-adic integers., Quantity is a property that can exist as a magnitude or multitude. Quantities can be compared in terms of "more", "less", or "equal", or by assigning a numerical value in terms of a unit of measurement. Quantity is among the basic classes of things along with quality, substance, change, and relation. Some quantities are such by their inner nature (as number), while others are functioning as states (properties, dimensions, attributes) of things such as heavy and light, long and short, broad and narrow, small and great, or much and little. A small quantity is sometimes referred to as a quantulum., In mathematics, a polynomial is an expression consisting of variables (or indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents. An example of a polynomial of a single indeterminate is . An example in three variables is ., In mathematics, especially in the field of abstract algebra, a polynomial ring or polynomial algebra is a ring (which is also a commutative algebra) formed from the set of polynomials in one or more indeterminates (traditionally also called variables) with coefficients in another ring, often a field. Polynomial rings have influenced much of mathematics, from the Hilbert basis theorem, to the construction of splitting fields, and to the understanding of a linear operator. Many important conjectures involving polynomial rings, such as Serre's problem, have influenced the study of other rings, and have influenced even the definition of other rings, such as group rings and rings of formal power series., In algebra, which is a broad division of mathematics, abstract algebra (occasionally called modern algebra) is the study of algebraic structures. Algebraic structures include groups, rings, fields, modules, vector spaces, lattices, and algebras. The term "abstract algebra" was coined in the early 20th century to distinguish this area of study from the other parts of algebra., 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 Algebraic number theory, an algebraic integer is a complex number that is a root of some monic polynomial (a polynomial whose leading coefficient is 1) with coefficients in formula_1 (the set of integers). The set of all algebraic integers, , is closed under addition and multiplication and therefore is a commutative subring of the complex numbers. The ring is the integral closure of regular integers formula_1 in complex numbers., In mathematics , specifically commutative algebra , Hilbert 's basis theorem says that a polynomial ring over a Noetherian ring is Noetherian ., Algebra (from Arabic ""al-jabr"" meaning "reunion of broken parts") is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics. As such, it includes everything from elementary equation solving to the study of abstractions such as groups, rings, and fields. The more basic parts of algebra are called elementary algebra, the more abstract parts are called abstract algebra or modern algebra. Elementary algebra is generally considered to be essential for any study of mathematics, science, or engineering, as well as such applications as medicine and economics. Abstract algebra is a major area in advanced mathematics, studied primarily by professional mathematicians., In algebra, a group ring is a free module and at the same time a ring, constructed in a natural way from any given ring and any given group. As a free module, its ring of scalars is the given ring, and its basis is one-to-one with the given group. As a ring, its addition law is that of the free module and its multiplication extends "by linearity" the given group law on the basis. Less formally, a group ring is a generalization of a given group, by attaching to each element of the group a "weighting factor" from a given ring., An integer (from the Latin "integer" meaning "whole") is a number that can be written without a fractional component. For example, 21, 4, 0, and 2048 are integers, while 9.75, , and  are not., In mathematics, more specifically in the area of abstract algebra known as ring theory, a Noetherian ring is a ring that satisfies the ascending chain condition on ideals; that is, given any chain of ideals:, In mathematics, the ascending chain condition (ACC) and descending chain condition (DCC) are finiteness properties satisfied by some algebraic structures, most importantly ideals in certain commutative rings. These conditions played an important role in the development of the structure theory of commutative rings in the works of David Hilbert, Emmy Noether, and Emil Artin.
The conditions themselves can be stated in an abstract form, so that they make sense for any partially ordered set. This point of view is useful in abstract algebraic dimension theory due to Gabriel and Rentschler., Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical problems about these sets of zeros., Space is the boundless three-dimensional extent in which objects and events have relative position and direction. Physical space is often conceived in three linear dimensions, although modern physicists usually consider it, with time, to be part of a boundless four-dimensional continuum known as spacetime. The concept of space is considered to be of fundamental importance to an understanding of the physical universe. However, disagreement continues between philosophers over whether it is itself an entity, a relationship between entities, or part of a conceptual framework., Subject: hilbert's basis theorem, Relation: named_after, Options: (A) 1 (B) 4 (C) 9 (D) concept (E) david hilbert (F) emmy noether (G) geometry (H) mathematics (I) measurement (J) p (K) point (L) sense (M) time

Answer:
david hilbert