Question

Ted Kaczynski’s first published work was a short proof of this theorem. For 10 points each:
[10h] Name this theorem also proved in chapter six of Proofs from THE BOOK. It states that all finite division rings are fields.
ANSWER: Wedderburn’s little theorem [or Wedderburn’s theorem]
[10e] In fields, multiplication always has this property. The group operation has this property in Abelian groups.
ANSWER: commutative [or commutativity; accept word forms of commute]
[10m] This mathematician also published a proof of Wedderburn’s little theorem. Rings named for this mathematician satisfy the descending chain condition, which is a stronger condition than the ascending chain condition satisfied by Noetherian rings.
ANSWER: Emil Artin [accept Artinian ring or Artin ring]
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GeodesicMTSU010010