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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 Whitehead's lemma ： ウィキペディア英語版 Whitehead's lemma : Whitehead's lemma is a technical result in abstract algebra used in algebraic K-theory. It states that a matrix of the form :$$ \begin u & 0 \\ 0 & u^ \end is equivalent to the identity matrix by elementary transformations (that is, transvections): :$$ \begin u & 0 \\ 0 & u^ \end = e_(u^) e_(1-u) e_(-1) e_(1-u^). Here, $e\_(s)$ indicates a matrix whose diagonal block is $1$ and $ij^$ entry is $s$. The name "Whitehead's lemma" also refers to the closely related result that the derived group of the stable general linear group is the group generated by elementary matrices. In symbols, :$\backslash operatorname(A)\; =\; ()$. This holds for the stable group (the direct limit of matrices of finite size) over any ring, but not in general for the unstable groups, even over a field. For instance for :$\backslash operatorname(2,\backslash mathbb/2\backslash mathbb)$ one has: : where Alt(3) and Sym(3) denote the alternating resp. symmetric group on 3 letters. ==See also== *Special linear group#Relations to other subgroups of GL(n,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「Whitehead's lemma」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.