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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Hochschild cohomology ： ウィキペディア英語版 Hochschild homology In mathematics, Hochschild homology (and cohomology) is a homology theory for associative algebras over rings. There is also a theory for Hochschild homology of certain functors. Hochschild cohomology was introduced by for algebras over a field, and extended to algebras over more general rings by . ==Definition of Hochschild homology of algebras== Let ''k'' be a ring, ''A'' an associative ''k''-algebra, and ''M'' an ''A''-bimodule. The enveloping algebra of ''A'' is the tensor product ''Ae''=''A''⊗''A''o of ''A'' with its opposite algebra. Bimodules over ''A'' are essentially the same as modules over the enveloping algebra of ''A'', so in particular ''A'' and ''M'' can be considered as ''Ae''-modules. defined the Hochschild homology and cohomology group of ''A'' with coefficients in ''M'' in terms of the Tor functor and Ext functor by :$HH\_n(A,M)\; =\; \backslash text\_n^(A,\; M)$ :$HH^n(A,M)\; =\; \backslash text^n\_(A,\; M)$ 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Hochschild homology」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.