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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 Engel identity ： ウィキペディア英語版 Engel identity The Engel identity, named after Friedrich Engel, is a mathematical equation that is satisfied by all elements of a Lie ring, in the case of an Engel Lie ring, or by all the elements of a group, in the case of an Engel group. The Engel identity is the defining condition of an Engel group. == Formal definition == A Lie ring $L$ is defined as a nonassociative ring with multiplication that is anticommutative and satisfies the Jacobi identity with respect to the Lie bracket $()$, defined for all elements $x,y$ in the ring $L$. The Lie ring $L$ is defined to be an n-Engel Lie ring if and only if * for all $x,\; y$ in $L$, the n-Engel identity $]\; =\; 0$ (n copies of $x$), is satisfied. In the case of a group $G$, in the preceding definition, use the definition and replace $0$ by $1$, where $1$ is the identity element of the group $G$. 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「Engel identity」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.