TASK DEFINITION: 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.
PROBLEM: One antagonist in this work leaves behind the head of Aeschere after killing him. Unferth argues that the success of this work's title character was due to luck. A villager steals a golden cup from a cave towards the end of this work. The title character  beheads the corpse of a figure who had been attacking Herot and decides to help King Hrothgar at its beginning. At the end of this work, Wiglaf helps the protagonist battle a dragon which ultimately kills the hero. For 10 points, name this epic poem about a hero who killed the monster Grendel.

SOLUTION: Literature

PROBLEM: 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

SOLUTION: Science

PROBLEM: They can be made from the reaction of organolithium reagents with aldehydes and ketones; the acid-catalyzed hydration of alkenes, ozymercuration-demecuration of alkenes, the reaction of Grignard reagents with aldehydes, esters, or ketones, or by the hydrolysis of alkyl halides. They can be converted to dialkyl ethers and are combined with carboxylic acids to undergo Fischer esterification. FTP name this group of organic compounds, composed of an OH group attached to a hydrocarbon group and symbolized as R-OH.

SOLUTION:
Science