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.
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© 2015 Springer International Publishing Switzerland
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Barot, M. (2015). Module Categories. In: Introduction to the Representation Theory of Algebras. Springer, Cham. https://doi.org/10.1007/978-3-319-11475-0_4
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DOI: https://doi.org/10.1007/978-3-319-11475-0_4
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Publisher Name: Springer, Cham
Print ISBN: 978-3-319-11474-3
Online ISBN: 978-3-319-11475-0
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