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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 Quotient algebra ： ウィキペディア英語版 Quotient algebra In mathematics, a quotient algebra, (where ''algebra'' is used in the sense of universal algebra), also called a factor algebra, is obtained by partitioning the elements of an algebra into equivalence classes given by a congruence relation, that is an equivalence relation that is additionally ''compatible'' with all the operations of the algebra, in the formal sense described below. == Compatible relation == Let ''A'' be a set (of the elements of an algebra $\backslash mathcal$), and let ''E'' be an equivalence relation on the set ''A''. The relation ''E'' is said to be ''compatible'' with (or have the ''substitution property'' with respect to) an ''n''-ary operation ''f'' if for all $a\_1,\; a\_2,\; \backslash ldots,\; a\_n,\; b\_1,\; b\_2,\; \backslash ldots,\; b\_n\; \backslash in\; A$ whenever $(a\_1,\; b\_1)\; \backslash in\; E,\; (a\_2,\; b\_2)\; \backslash in\; E,\; \backslash ldots,\; (a\_n,\; b\_n)\; \backslash in\; E$ implies $(f\; (a\_1,\; a\_2,\; \backslash ldots,\; a\_n),\; f\; (b\_1,\; b\_2,\; \backslash ldots,\; b\_n))\; \backslash in\; E$. An equivalence relation compatible with all the operations of an algebra is called a congruence. 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「Quotient algebra」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.