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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 Locally nilpotent ： ウィキペディア英語版 Locally nilpotent In the mathematical field of commutative algebra, an ideal ''I'' in a commutative ring ''A'' is locally nilpotent at a prime ideal ''p'' if ''I''''p'', the localization of ''I'' at ''p'', is a nilpotent ideal in ''A''''p''. In non-commutative algebra and group theory, an algebra or group is locally nilpotent if and only if every finitely generated subalgebra or subgroup is nilpotent. The subgroup generated by the normal locally nilpotent subgroups is called the Hirsch–Plotkin radical and is the generalization of the Fitting subgroup to groups without the ascending chain condition on normal subgroups. A locally nilpotent ring is one in which every finitely generated subring is nilpotent: locally nilpotent rings form a radical class, giving rise to the Levitzki radical. 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「Locally nilpotent」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.