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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'': :: 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
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