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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 Comodule ： ウィキペディア英語版 Comodule In mathematics, a comodule or corepresentation is a concept dual to a module. The definition of a comodule over a coalgebra is formed by dualizing the definition of a module over an associative algebra. ==Formal definition== Let ''K'' be a field, and ''C'' be a coalgebra over ''K''. A (right) comodule over ''C'' is a ''K''-vector space ''M'' together with a linear map :$\backslash rho\backslash colon\; M\; \backslash to\; M\; \backslash otimes\; C$ such that # $(\backslash mathrm\; \backslash otimes\; \backslash Delta)\; \backslash circ\; \backslash rho\; =\; (\backslash rho\; \backslash otimes\; \backslash mathrm)\; \backslash circ\; \backslash rho$ # $(\backslash mathrm\; \backslash otimes\; \backslash varepsilon)\; \backslash circ\; \backslash rho\; =\; \backslash mathrm$, where Δ is the comultiplication for ''C'', and ε is the counit. Note that in the second rule we have identified $M\; \backslash otimes\; K$ with $M\backslash ,$. 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「Comodule」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.