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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 Monoid ring ： ウィキペディア英語版 Monoid ring In abstract algebra, a monoid ring is a ring constructed from a ring and a monoid, just as a group ring is constructed from a ring and a group. ==Definition== Let ''R'' be a ring and let ''G'' be a monoid. The monoid ring or monoid algebra of ''G'' over ''R'', denoted ''R''() or ''RG'', is the set of formal sums $\backslash sum\_\; r\_g\; g$, where $r\_g\; \backslash in\; R$ for each $g\; \backslash in\; G$ and ''r''''g'' = 0 for all but finitely many ''g'', equipped with coefficient-wise addition, and the multiplication in which the elements of ''R'' commute with the elements of ''G''. More formally, ''R''() is the set of functions such that } is finite, equipped with addition of functions, and with multiplication defined by :$(\backslash phi\; \backslash psi)(g)\; =\; \backslash sum\_\; \backslash phi(k)\; \backslash psi(\backslash ell)$. If ''G'' is a group, then ''R''() is also called the group ring of ''G'' over ''R''. 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「Monoid ring」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.