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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–Samuel function ： ウィキペディア英語版 Hilbert–Samuel function In commutative algebra the Hilbert–Samuel function, named after David Hilbert and Pierre Samuel,〔H. Hironaka, Resolution of Singularities of an Algebraic Variety Over a Field of Characteristic Zero: I. Ann. of Math. 2nd Ser., Vol. 79, No. 1. (Jan., 1964), pp. 109-203.〕 of a nonzero finitely generated module $M$ over a commutative Noetherian local ring $A$ and a primary ideal $I$ of $A$ is the map $\backslash chi\_^:\backslash mathbb\backslash rightarrow\backslash mathbb$ such that, for all $n\backslash in\backslash mathbb$, :$\backslash chi\_^(n)=\backslash ell(M/I^M)$ where $\backslash ell$ denotes the length over $A$. It is related to the Hilbert function of the associated graded module $\backslash operatorname\_I(M)$ by the identity : $\backslash chi\_M^I\; (n)=\backslash sum\_^n\; H(\backslash operatorname\_I(M),i).$ For sufficiently large $n$, it coincides with a polynomial function of degree equal to $\backslash dim(\backslash operatorname\_I(M))$.〔Atiyah, M. F. and MacDonald, I. G. ''Introduction to Commutative Algebra''. Reading, MA: Addison–Wesley, 1969.〕 ==Examples== For the ring of formal power series in two variables $kx,y$ taken as a module over itself and graded by the order and the ideal generated by the monomials ''x''2 and ''y''3 we have : $\backslash chi(1)=1,\backslash quad\; \backslash chi(2)=3,\backslash quad\; \backslash chi(3)=5,\backslash quad\; \backslash chi(4)=6\backslash text\; \backslash chi(k)=6\backslash textk\; >\; 4.$〔 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–Samuel function」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.