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.

[EX Q]: 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
[EX A]: Science

[EX Q]: This dynasty sent Zhang Qian on exploring missions, and it was confronted by the Rebellion of the Seven States. The Records of A Grand Historian were written by Sima Qian during this dynasty, and after the Battle of Jushi, Emperor Wu forced the Xiongnu to become its tributaries. An interregnum by Wang Mang's Xin dynasty divides this dynasty into [*] "Eastern" and "Western" parts. It was founded by Liu Bang after the Qin dynasty and was followed by the Three Kingdoms period. Challenged by the palace eunuchs and the Daoist Yellow Turban Rebellion, for 10 points, name the Chinese dynasty after which the primary ethnic group of China is named.
[EX A]: History

[EX Q]: One film from this country sees an elderly couple travel to the city only to be shooed off by their children and uses almost exclusively low-angle stationary shots. In another film from here, the protagonist struggles to find her own "ghost" while leading Section 9 on a hunt for the Puppet Master. Ghost in the Shell is a film from this country, which also produced a film whose protagonist returns a cursed gold seal to Zeniba to cure her friend Haku. That character feeds copious amounts of food the spirit No-Face while attempting to save her parents, who have been transformed into pigs. For 10 points, name this country that produced Spirited Away.
[EX A]:
Social Science