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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 Invariant factors ： ウィキペディア英語版 Invariant factor The invariant factors of a module over a principal ideal domain (PID) occur in one form of the structure theorem for finitely generated modules over a principal ideal domain. If $R$ is a PID and $M$ a finitely generated $R$-module, then :$M\backslash cong\; R^r\backslash oplus\; R/(a\_1)\backslash oplus\; R/(a\_2)\backslash oplus\backslash cdots\backslash oplus\; R/(a\_m)$ for some integer $r\backslash geq0$ and a (possibly empty) list of nonzero elements $a\_1,\backslash ldots,a\_m\backslash in\; R$ for which $a\_1\; \backslash mid\; a\_2\; \backslash mid\; \backslash cdots\; \backslash mid\; a\_m$. The nonnegative integer $r$ is called the ''free rank'' or ''Betti number'' of the module $M$, while $a\_1,\backslash ldots,a\_m$ are the ''invariant factors'' of $M$ and are unique up to associatedness. The invariant factors of a matrix over a PID occur in the Smith normal form and provide a means of computing the structure of a module from a set of generators and relations. ==See also== * Elementary divisors 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「Invariant factor」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.