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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 Discrete valuation ： ウィキペディア英語版 Discrete valuation In mathematics, a discrete valuation is an integer valuation on a field ''K'', that is a function :$\backslash nu:K\backslash to\backslash mathbb\; Z\backslash cup\backslash$ satisfying the conditions :$\backslash nu(x\backslash cdot\; y)=\backslash nu(x)+\backslash nu(y)$ :$\backslash nu(x+y)\backslash geq\backslash min\backslash big\backslash$ :$\backslash nu(x)=\backslash infty\backslash iff\; x=0$ for all $x,y\backslash in\; K$. Note that often the trivial valuation which takes on only the values $0,\backslash infty$ is explicitly excluded. A field with a non-trivial discrete valuation is called a discrete valuation field. ==Discrete valuation rings and valuations on fields== To every field with discrete valuation $\backslash nu$ we can associate the subring ::$\backslash mathcal\_K\; :=\; \backslash left\backslash$ of $K$, which is a discrete valuation ring. Conversely, the valuation $\backslash nu:\; A\; \backslash rightarrow\; \backslash Z\backslash cup\backslash$ on a discrete valuation ring $A$ can be extended in a unique way to a discrete valuation on the quotient field $K=\backslash text(A)$; the associated discrete valuation ring $\backslash mathcal\_K$ is just $A$. 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「Discrete valuation」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.