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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 Bimodule ： ウィキペディア英語版 Bimodule In abstract algebra, a bimodule is an abelian group that is both a left and a right module, such that the left and right multiplications are compatible. Besides appearing naturally in many parts of mathematics, bimodules play a clarifying role, in the sense that many of the relationships between left and right modules become simpler when they are expressed in terms of bimodules. == Definition == If ''R'' and ''S'' are two rings, then an ''R''-''S''-bimodule is an abelian group ''M'' such that: # ''M'' is a left ''R''-module and a right ''S''-module. # For all ''r'' in ''R'', ''s'' in ''S'' and ''m'' in ''M'': ::$(rm)s\; =\; r(ms)\; .$ An ''R''-''R''-bimodule is also known as an ''R''-bimodule. 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「Bimodule」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.