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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 Stably finite ring ： ウィキペディア英語版 Stably finite ring In algebra, a ring $R$ is said to be stably finite (or weakly finite) if, for all square matrices ''A'', ''B'' of the same size over ''R'', ''AB'' = 1 implies ''BA'' = 1. This is a slightly stronger property for a ring than its having the invariant basis number: any nontrivial〔A trivial ring is stably finite but doesn't have IBN.〕 stably finite ring has IBN. Commutative rings, noetherian rings and artinian rings are stably finite. A subring of a stably finite ring and a matrix ring over a stably finite ring is stably finite. A ring satisfying Klein's nilpotence condition is stably finite. ==References== * P.M. Cohn (2003). Basic Algebra, Springer. 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「Stably finite ring」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.