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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 Witt vector ： ウィキペディア英語版 Witt vector In mathematics, a Witt vector is an infinite sequence of elements of a commutative ring. Ernst Witt showed how to put a ring structure on the set of Witt vectors, in such a way that the ring of Witt vectors over the finite field of order ''p'' is the ring of ''p''-adic integers. ==Motivation== Any $p$-adic integer (an element of $\backslash mathbb\_p$) can be written as a power series $a\_0\; +\; a\_1\; p^1\; +\; a\_2\; p^2\; +\; \backslash cdots$, where the $a$'s are usually taken from the set $\backslash$. However, it is hard to figure out an algebraic expression for addition and multiplication, as one faces the problem of carry. Luckily, this set of representatives is not the only possible choice, and Teichmüller suggested an alternative set consisting of 0 together with the $p-1$st roots of $1$: in other words, the $p$ roots of :$x^p\; -\; x\; =\; 0$ in $\backslash mathbb\_p$. These Teichmüller representatives can be identified with the elements of the finite field $\backslash mathbb\_p$ of order $p$ (by taking residues modulo $p$), and elements of $\backslash mathbb\_p^\backslash times$ are taken to their representatives by the Teichmüller character $\backslash omega:\backslash mathbb\_p^\backslash times\; \backslash rightarrow\; \backslash mathbb\_p^\backslash times$. This identifies the set of $p$-adic integers with infinite sequences of elements of $\backslash omega(\backslash mathbb\_p^\backslash times)\; \backslash cup\; \backslash$. We now have the following problem: given two infinite sequences of elements of $\backslash omega(\backslash mathbb\_p^\backslash times)\; \backslash cup\; \backslash$, describe their sum and product as $p$-adic integers explicitly. This problem was solved by Witt using Witt vectors. 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「Witt vector」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.