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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 Fitting ideal ： ウィキペディア英語版 Fitting ideal In commutative algebra, the Fitting ideals of a finitely generated module over a commutative ring describe the obstructions to generating the module by a given number of elements. They were introduced by . ==Definition== If ''M'' is a finitely generated module over a commutative ring ''R'' generated by elements ''m''1,...,''m''''n'' with relations :$a\_m\_1+\backslash cdots\; +\; a\_m\_n=0\backslash \; (\backslash textj\; =\; 1,\; 2,\; \backslash dots)\backslash ,$ then the ''i''th Fitting ideal Fitt''i''(''M'') of ''M'' is generated by the minors (determinants of submatrices) of order ''n'' − ''i'' of the matrix ''a''''jk''. The Fitting ideals do not depend on the choice of generators and relations of ''M''. Some authors defined the Fitting ideal ''I''(''M'') to be the first nonzero Fitting ideal Fitt''i''(''M''). 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「Fitting ideal」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.