In this task you will be given a text passage from a trivia quiz. You should choose the category this question belongs to from these categories: History, Science, Social Science, Fine Arts, Literature. You can only choose one category, so if in doubt, please choose the closest match.

The Hilbert Basis Theorem guarantees that if one of these is Noetherian, then the polynomials over it are also Noetherian. While the existence of a multiplicative unit in one of these isnt guaranteed by the axioms, most authors assume its presence. These can form quotients with special subsets known as ideals, and commutative ones with no zero divisors are known as integral domains. Formally an abelian group over addition and a monoid over multiplication, this describes, for ten points, what algebraic structure exemplified by the integers
Science

Ninhydrin forms a Schiff base with this chemical, resulting in a hue known as Ruhemanns purple. The Birch reduction takes place in a liquid substrate of it, the reason it is common in methamphetamine labs. The Kjeldahl method uses this molecule as an end-product to measure the amount of nitrogen in a sample, and it is oxidized in the first step of a nitric acid forming procedure, the Ostwald process. For 10 points, name this weak base found in fertilizers, formed by combining hydrogen and nitrogen in a three-to-one ratio in the Haber process.
Science

This country's "National Rainbow Coalition" was ended by a 2005 referendum in which "yes" and "no" votes were represented by bananas and oranges respectively. That referendum spawned this country's Orange Democratic Movement, which is led by Prime Minister Raila Odinga. Odinga recently entered into a power sharing agreement with President Mwai Kibaki after the violent aftermath of the 2007 elections. For 10 points, name this African country with capital at Naiobi.

History