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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 Steinberg symbol ： ウィキペディア英語版 Steinberg symbol In mathematics a Steinberg symbol is a pairing function which generalises the Hilbert symbol and plays a role in the algebraic K-theory of fields. It is named after mathematician Robert Steinberg. For a field ''F'' we define a ''Steinberg symbol'' (or simply a ''symbol'') to be a function $(\; \backslash cdot\; ,\; \backslash cdot\; )\; :\; F^$ * \times F^ * \rightarrow G, where ''G'' is an abelian group, written multiplicatively, such that * $(\; \backslash cdot\; ,\; \backslash cdot\; )$ is bimultiplicative; * if $a+b\; =\; 1$ then $(a,b)\; =\; 1$. The symbols on ''F'' derive from a "universal" symbol, which may be regarded as taking values in $F^$ * \otimes F^ * / \langle a \otimes 1-a \rangle. By a theorem of Matsumoto, this group is $K\_2\; F$ and is part of the Milnor K-theory for a field. ==Properties== If (⋅,⋅) is a symbol then (assuming all terms are defined) * $(a,\; -a)\; =\; 1$; * $(b,\; a)\; =\; (a,\; b)^$; * $(a,\; a)\; =\; (a,\; -1)$ is an element of order 1 or 2; * $(a,\; b)\; =\; (a+b,\; -b/a)$. 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「Steinberg symbol」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.