翻訳と辞書 Words near each other ・ Radical Left Front ・ Radical lesbians ・ Radical Liberal Party ・ Radical Liberal Party (Luxembourg) ・ Radical Liberal Party (Paraguay) ・ Radical Light ・ Radical Love ・ Radical Loving Care ・ Radical mastectomy ・ Radical media ・ Radical Mestizo ・ Radical Movement of Social Democratic Alliance ・ Radical nationalism in Russia ・ Radical Network ・ Radical of a Lie algebra ・ Radical of a module ・ Radical of a ring ・ Radical of an algebraic group ・ Radical of an ideal ・ Radical of an integer ・ Radical Orthodoxy ・ Radical Outdoor Challenge ・ Radical Party ・ Radical Party (Bolivia) ・ Radical Party (Chile) ・ Radical Party (France) ・ Radical Party (Italy) ・ Radical Party (Italy, 1877) ・ Radical Party (New Zealand) ・ Radical Party of Chile Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Radical of a module ： ウィキペディア英語版 Radical of a module In mathematics, in the theory of modules, the radical of a module is a component in the theory of structure and classification. It is a generalization of the Jacobson radical for rings. In many ways, it is the dual notion to that of the socle soc(''M'') of ''M''. ==Definition== Let ''R'' be a ring and ''M'' a left ''R''-module. A submodule ''N'' of ''M'' is called maximal or cosimple if the quotient ''M''/''N'' is a simple module. The radical of the module ''M'' is the intersection of all maximal submodules of ''M'', :$\backslash mathrm\; (M)\; =\; \backslash bigcap\; \backslash \; \backslash ,$ Equivalently, :$\backslash mathrm\; (M)\; =\; \backslash sum\; \backslash \; \backslash ,$ These definitions have direct dual analogues for soc(''M''). 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「Radical of a module」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.