Almost laura algebras. (English) Zbl 1178.16007
Summary: We propose a generalization for the class of laura algebras, called almost laura. We show that this new class of algebras retains most of the essential features of laura algebras, especially concerning the important role played by the non-semiregular components in their Auslander-Reiten quivers. Also, we study more intensively the left supported almost laura algebras, showing that these are characterized by the presence of a generalized standard, convex and faithful component. Finally, we prove that almost laura algebras behave well with respect to full subcategories, split-by-nilpotent extensions and skew group algebras.
MSC:
| 16E30 | Homological functors on modules (Tor, Ext, etc.) in associative algebras |
| 16G70 | Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers |
| 16E10 | Homological dimension in associative algebras |
| 16G10 | Representations of associative Artinian rings |
Keywords:
almost laura algebras; infinite radical; left supported algebras; skew group algebras; Auslander-Reiten quivers; Artin algebras; indecomposable injective modules; quasi-tilted algebras; generalized standard componentsReferences:
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