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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 Divided power structure ： ウィキペディア英語版 Divided power structure In mathematics, specifically commutative algebra, a divided power structure is a way of making expressions of the form $x^n\; /\; n!$ meaningful even when it is not possible to actually divide by $n!$. == Definition == Let ''A'' be a commutative ring with an ideal ''I''. A divided power structure (or PD-structure, after the French ''puissances divisées'') on ''I'' is a collection of maps $\backslash gamma\_n\; :\; I\; \backslash to\; A$ for ''n''=0, 1, 2, ... such that: #$\backslash gamma\_0(x)\; =\; 1$ and $\backslash gamma\_1(x)\; =\; x$ for $x\; \backslash in\; I$, while $\backslash gamma\_n(x)\; \backslash in\; I$ for ''n'' > 0. #$\backslash gamma\_n(x\; +\; y)\; =\; \backslash sum\_^n\; \backslash gamma\_(x)\; \backslash gamma\_i(y)$ for $x,\; y\; \backslash in\; I$. #$\backslash gamma\_n(\backslash lambda\; x)\; =\; \backslash lambda^n\; \backslash gamma\_n(x)$ for $\backslash lambda\; \backslash in\; A,\; x\; \backslash in\; I$. #$\backslash gamma\_m(x)\; \backslash gamma\_n(x)\; =\; ((m,\; n))\; \backslash gamma\_(x)$ for $x\; \backslash in\; I$, where $((m,\; n))\; =\; \backslash frac$ is an integer. #$\backslash gamma\_n(\backslash gamma\_m(x))\; =\; C\_\; \backslash gamma\_(x)$ for $x\; \backslash in\; I$, where $C\_\; =\; \backslash frac$ is an integer. For convenience of notation, $\backslash gamma\_n(x)$ is often written as $x^$ when it is clear what divided power structure is meant. The term ''divided power ideal'' refers to an ideal with a given divided power structure, and ''divided power ring'' refers to a ring with a given ideal with divided power structure. Homomorphisms of divided power algebras are ring homomorphisms that respects the divided power structure on its source and target. 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「Divided power structure」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.