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.
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Question: 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

Answer: Science


Question: The reciprocal relationship between the eigenvalues of the mass matrix of these particles is called the "seesaw mechanism"; the larger eigenvalue may be the mass of their "sterile" variety. One phenomenon predicted by Pontecorvo involving these entities was searched for by (*) MINOS. Reines and Cowan used an aqueous cadmium chloride solution to detect them, and other detectors tend to include large volumes of material, such as Super Kamiokande. For 10 points, name these leptons, the nearly massless products of radioactive decay whose varieties include the muon and tau and which are represented by the letter nu.

Answer: Science


Question: [AR] In order to avoid hydrolysis of the initial reactant strong bases such as Lithium diisopropylamide must be used and final intermediate must be neutralized by an aqueous acid in order to obtain the final product. The classic version of this reaction has one enolizable reactant while a variation involving aryl aldehydes has this reaction's namesake appended with Schmidt. The Stobbe modification is specifically for the diethyl ester of succinic acid and a related reaction using alpha-halo esters is known as the Darzens reaction, while an intramolecular version of this reaction is known as the Dieckman Reaction, which readily creates five or six membered rings. For 10 points, name this eponymous condensation reaction involving esters or ketones conducted in the presence of sodium ethoxide to yield beta-ketoesters.

Answer:
Science