Auslander-Reiten components containing modules of finite complexity
Master thesis
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http://hdl.handle.net/11250/258876Utgivelsesdato
2011Metadata
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Sammendrag
Let R be a connected selfinjective Artin algebra. We prove that any almost split sequence ending at an Omega-perfect R-module of finite complexity has at most four non-projective summands in a chosen decomposition of the middle term into indecomposable modules. Moreover, we show that a chosen decomposition into indecomposable modules of the middle term of an almost split sequence ending at an R-module of complexity 1 lying in a regular component of the Auslander-Reiten quiver has at most two summands. Furthermore, we prove that the regular component is of type ZA_{infinity} or ZA_{infinity}/. We use this to study modules with eventually constant and eventually periodic Betti numbers.