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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 Support of a module ： ウィキペディア英語版 Support of a module In commutative algebra, the support of a module ''M'' over a commutative ring ''A'' is the set of all prime ideals $\backslash mathfrak$ of ''A'' such that $M\_\backslash mathfrak\; \backslash ne\; 0$.〔EGA 0I, 1.7.1.〕 It is denoted by $\backslash operatorname(M)$. In particular, $M\; =\; 0$ if and only if its support is empty. * Let $0\; \backslash to\; M\text{'}\; \backslash to\; M\; \backslash to\; M\text{'}\text{'}\; \backslash to\; 0$ be an exact sequence of ''A''-modules. Then *:$\backslash operatorname(M)\; =\; \backslash operatorname(M\text{'})\; \backslash cup\; \backslash operatorname(M\text{'}\text{'}).$ * If $M$ is a sum of submodules $M\_\backslash lambda$, then $\backslash operatorname(M)\; =\; \backslash cup\_\backslash lambda\; \backslash operatorname(M\_\backslash lambda).$ * If $M$ is a finitely generated ''A''-module, then $\backslash operatorname(M)$ is the set of all prime ideals containing the annihilator of ''M''. In particular, it is closed. *If $M,\; N$ are finitely generated ''A''-modules, then *:$\backslash operatorname(M\; \backslash otimes\_A\; N)\; =\; \backslash operatorname(M)\; \backslash cap\; \backslash operatorname(N).$ *If $M$ is a finitely generated ''A''-module and ''I'' is an ideal of ''A'', then $\backslash operatorname(M/IM)$ is the set of all prime ideals containing $I\; +\; \backslash operatorname(M).$ This is $V(I)\backslash cap\; \backslash operatorname(M)$. ==See also== *Associated prime 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「Support of a module」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.