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 |
Keywords:
Auslander-Reiten quivers; generalized multicoils; Euler forms; tame algebras; indecomposable modules; coherent components; finite dimensional algebrasReferences:
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