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abelian categories with applications to rings and modules

[ Last edited by javeey on 2010-5-8 at 17:13 ]
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1 Assume that $A$ is a finite dimensional $K$-algebra£¬and $M$ a finitely generated indecomposable module, then the socle $socM $ of $M$ is simple£¬why?

2 Assume that $A$ is a finite dimensional $K$-algebra£¬and $M$ a finitely generated  module, is the injective envelope of $M$ finitely generated? why?


3 Assume that $A$ is a finite dimensional $K$-algebra£¬and $M$ a finitely generated indecomposable  module, is the injective envelope of $M$ indecomposable? why?

[ Last edited by xuaimin88888 on 2012-10-23 at 16:17 ]
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