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On the indecomposable modules in almost cyclic coherent Auslander-Reiten components. (English) Zbl 1260.16013

Summary: We establish an inequality between the dimensions of the endomorphism and extension spaces of the indecomposable modules in generalized standard almost cyclic coherent components of the Auslander-Reiten quivers of finite dimensional algebras over an arbitrary base field. As an application we provide a homological characterization, involving the Euler quadratic form, of the tame algebras with separating families of almost cyclic coherent Auslander-Reiten components.

MSC:

16G10 Representations of associative Artinian rings
16E30 Homological functors on modules (Tor, Ext, etc.) in associative algebras
16G70 Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers
16G60 Representation type (finite, tame, wild, etc.) of associative algebras
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