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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'', : Equivalently, : 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
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