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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 Standard complex ： ウィキペディア英語版 Standard complex In mathematics, the standard complex, also called standard resolution, bar resolution, bar complex, bar construction, is a way of constructing resolutions in homological algebra. It was first introduced for the special case of algebras over a commutative ring by and and has since been generalized in many ways. The name "bar complex" comes from the fact that used a vertical bar | as a shortened form of the tensor product ⊗ in their notation for the complex. ==Definition== If ''A'' is an associative algebra over a field ''K'', the standard complex is :$\backslash cdots\backslash rightarrow\; A\backslash otimes\; A\backslash otimes\; A\backslash rightarrow\; A\backslash otimes\; A\backslash rightarrow\; A\; \backslash rightarrow\; 0\backslash ,,$ with the differential given by :$d(a\_0\backslash otimes\; \backslash cdots\backslash otimes\; a\_)=\backslash sum\_^n\; (-1)^i\; a\_0\backslash otimes\backslash cdots\backslash otimes\; a\_ia\_\backslash otimes\backslash cdots\backslash otimes\; a\_\backslash ,.$ If ''A'' is a unital ''K''-algebra, the standard complex is exact. $(A\backslash otimes\; A\backslash otimes\; A\backslash rightarrow\; A\backslash otimes\; A)$ is a free ''A''-bimodule resolution of the ''A''-bimodule ''A''. 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「Standard complex」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.