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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 Hilbert–Burch theorem ： ウィキペディア英語版 Hilbert–Burch theorem In mathematics, the Hilbert–Burch theorem describes the structure of some free resolutions of a quotient of a local or graded ring in the case that the quotient has projective dimension 2. proved a version of this theorem for polynomial rings, and proved a more general version. Several other authors later rediscovered and published variations of this theorem. gives a statement and proof. ==Statement== If ''R'' is a local ring with an ideal ''I'' and :$0\; \backslash rightarrow\; R^m\backslash rightarrow\; R^n\; \backslash rightarrow\; R\; \backslash rightarrow\; R/I\backslash rightarrow\; 0$ is a free resolution of the ''R''-module ''R''/''I'', then ''m'' = ''n'' – 1 and the ideal ''I'' is ''aJ'' where ''a'' is a non zero divisor of ''R'' and ''J'' is the depth 2 ideal generated by the determinants of the minors of size ''m'' of the matrix of the map from ''R''''m'' to ''R''''n''. 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「Hilbert–Burch theorem」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.