Short Chains and Regular Components

DOI10.2307/2159116zbMath0782.16008OpenAlexW4236838174MaRDI QIDQ4695546

Sverre O. Smalø, Idun Reiten, Andrzej Skowroński

Publication date: 29 June 1993

Full work available at URL: https://doi.org/10.2307/2159116

zbMATH Keywords

annihilatorquiverArtin algebrashort chainsregular componentstilted algebraregular tilting modulenondirecting moduleswild, hereditary algebra

Mathematics Subject Classification ID

Module categories in associative algebras (16D90) Homological functors on modules (Tor, Ext, etc.) in associative algebras (16E30) Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers (16G70) Representations of quivers and partially ordered sets (16G20) Representations of associative Artinian rings (16G10)

Related Items (5)

On the number of terms in the middle of almost split sequences over cycle-finite Artin algebras. ⋮ Tilted algebras and generalized standard Auslander-Reiten components ⋮ Another characterization of tilted algebras. ⋮ Quasitilted one-point extensions of wild hereditary algebras ⋮ Stable equivalence of selfinjective Artin algebras of Dynkin type.

Cites Work

• On the derived category of a finite-dimensional algebra
• A characterization of finite Auslander-Reiten quivers
• Modules determined by their composition factors
• Tame algebras and integral quadratic forms
• Wild hereditary Artin algebras and linear methods
• Generalization of Yamagata's theorem on trivial extensions
• The regular components of the Auslander-Reiten quiver of a tilted algebra
• Covering spaces in representation-theory
• Directing modules
• Trivial Extensions of Tilted Algebras
• A Characterization of a New Class of Artin Algebras
• The Structure of Stable Components
• Short Chains and Short Cycles of Modules
• Indecomposable representations of graphs and algebras
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