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xuaimin88888新虫 (初入文坛)
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[求助]
请教三个代数问题 the socle and injective envelope of indecomposable modules
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请教三个代数问题 the socle and injective envelope of indecomposable modules 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? |
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