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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 Deviation of a local ring ： ウィキペディア英語版 Deviation of a local ring In commutative algebra, the deviations of a local ring ''R'' are certain invariants ε''i''(''R'') that measure how far the ring is from being regular. ==Definition== The deviations ε''n'' of a local ring ''R'' with residue field ''k'' are non-negative integers defined in terms of its Poincaré series ''P''(''x'') by : $P(x)=\backslash sum\_x^n\; \backslash operatorname^R\_n(k,k)\; =\; \backslash prod\_\; \backslash frac\}\}\}\}.$ The zeroth deviation ε0 is the embedding dimension of ''R'' (the dimension of its tangent space). The first deviation ε1 vanishes exactly when the ring ''R'' is a regular local ring, in which case all the higher deviations also vanish. The second deviation ε2 vanishes exactly when the ring ''R'' is a complete intersection ring, in which case all the higher deviations vanish. 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「Deviation of a local ring」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.