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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 Loewy ring ： ウィキペディア英語版 Loewy ring In mathematics, a Loewy ring or semi-Artinian ring is a ring in which every non-zero module has a non-zero socle, or equivalently if the Loewy length of every module is defined. The concepts are named after Alfred Loewy. ==Loewy length== The Loewy length and Loewy series were introduced by If ''M'' is a module, then define the Loewy series ''M''α for ordinals α by ''M''0 = 0, ''M''α+1/''M''α = socle ''M''/''M''α, ''M''α = ∪λ<α ''M''λ if α is a limit ordinal. The Loewy length of ''M'' is defined to be the smallest α with ''M'' = ''M''α, if it exists. 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「Loewy 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.