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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 Amitsur–Levitzki theorem ： ウィキペディア英語版 Amitsur–Levitzki theorem In algebra, the Amitsur–Levitzki theorem states that the algebra of ''n'' by ''n'' matrices satisfies a certain identity of degree 2''n''. It was proved by . In particular matrix rings are polynomial identity rings such that the smallest identity they satisfy has degree exactly 2''n''. ==Statement== The standard polynomial of degree ''n'' is :$S\_n(x\_1,\backslash ldots,x\_n)\; =\; \backslash sum\_(\backslash sigma)x\_\backslash cdots\; x\_\; \backslash$ in non-commutative variables ''x''1,...,''x''''n'', where the sum is taken over all ''n''! elements of the symmetric group ''S''''n''. The Amitsur–Levitzki theorem states that for ''n'' by ''n'' matrices ''A''1,...,''A''2''n'' then :$S\_(A\_1,\backslash ldots,A\_)\; =\; 0\; \backslash \; .$ 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「Amitsur–Levitzki theorem」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.