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

Aleksandr Benckendorff was charged with hunting them down, and many had been members of the Union of Salvation and the Union of Welfare. Five of them were officially executed including Pavel Pestel who organized the Southern Society and the poet Kondraty Ryelev who hoped that his Northern faction's refusal to support Nicholas I's ascension would spark an uprising that would leave Prince Trubestkoy as dictator. FTP identify this mostly upper-class group of Russian revolutionaries whose 1825 rebellion failed and who are named for the month in which their aborted operations took place.
History

The blende of this element is used as a model crystal structure for semiconductors like indium
phosphide. In one reaction, this element is used with alpha-halo esters to condense ketones or aldehydes to
form beta-hydroxy-esters. When coupled with copper, this element reacts with alkenes to yield a
cyclopropane. Those reactions are named for Reformatsky and Simmons-Smith. Found in the ore
sphalerite, this element and hydrochloric acid reduce ketones to alkanes in the Clemmensen reduction. In
proteins, this element makes "gag-knuckles," "treble-clefs," and other structures known as "fingers."
Galvanized steel is coated in this element, and brass is an alloy of copper and this element. For 10 points,
name this element with number 30 and symbol Zn.
Science