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Erschienen in:
2015 | OriginalPaper | Buchkapitel
4. Module Categories
verfasst von : Michael Barot
Erschienen in: Introduction to the Representation Theory of Algebras
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Abstract
The focus is now changed towards modules. It is shown, that in our context the decomposition of a module into indecomposable summands is essentially unique. Several categorical notions for modules are developed: projective and injective, simple and semisimple modules are defined. In each case a full characterization of indecomposable modules with that particular property is achieved. This is a first step towards understanding the structure of module categories.