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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 congruence relation ： ウィキペディア英語版 congruence relation In abstract algebra, a congruence relation (or simply congruence) is an equivalence relation on an algebraic structure (such as a group, ring, or vector space) that is compatible with the structure. Every congruence relation has a corresponding quotient structure, whose elements are the equivalence classes (or congruence classes) for the relation. ==Basic example== The prototypical example of a congruence relation is congruence modulo $n$ on the set of integers. For a given positive integer $n$, two integers $a$ and $b$ are called congruent modulo $n$, written : $a\; \backslash equiv\; b\; \backslash pmod$ if $a\; -\; b$ is divisible by $n$ (or equivalently if $a$ and $b$ have the same remainder when divided by $n$). for example, $37$ and $57$ are congruent modulo $10$, : $37\; \backslash equiv\; 57\; \backslash pmod$ since $37\; -\; 57\; =\; -20$ is a multiple of 10, or equivalently since both $37$ and $57$ have a remainder of $7$ when divided by $10$. Congruence modulo $n$ (for a fixed $n$) is compatible with both addition and multiplication on the integers. That is, if : $a\_1\; \backslash equiv\; a\_2\; \backslash pmod$ and $b\_1\; \backslash equiv\; b\_2\; \backslash pmod$ then : $a\_1\; +\; b\_1\; \backslash equiv\; a\_2\; +\; b\_2\; \backslash pmod$ and $a\_1\; b\_1\; \backslash equiv\; a\_2b\_2\; \backslash pmod$ The corresponding addition and multiplication of equivalence classes is known as modular arithmetic. From the point of view of abstract algebra, congruence modulo $n$ is a congruence relation on the ring of integers, and arithmetic modulo $n$ occurs on the corresponding quotient ring. 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「congruence relation」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.