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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 change of rings ： ウィキペディア英語版 change of rings In algebra, given a ring homomorphism $f:\; R\; \backslash to\; S$, there are three ways to change the coefficient ring of a module; namely, for a right ''R''-module ''M'' and a right ''S''-module ''N'', *$f\_!\; M\; =\; M\; \backslash otimes\_R\; S$, the induced module. *$f\_$ * M = \operatorname_R(S, M), the coinduced module. *$f^$ * N = N_R, the restriction of scalars. They are related as adjoint functors: :$f\_!\; :\; \backslash text\_R\; \backslash leftrightarrows\; \backslash text\_S\; :\; f^$ * and :$f^$ * : \text_S \leftrightarrows \text_R : f_ *. This is related to Shapiro's lemma. ==Restriction of scalars== Restriction of scalars changes ''S''-modules into ''R''-modules. In algebraic geometry, the term "restriction of scalars" is often used as a synonym for Weil restriction. 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「change of rings」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.