On the Number of DTr-Orbits Containing Directing Modules

DOI10.2307/2160117zbMath0787.16014OpenAlexW4244641561MaRDI QIDQ4201604

Jie Xiao, Liangang Peng

Publication date: 1 September 1993

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2160117

zbMATH Keywords

Auslander-Reiten quiverArtin algebraAuslander-Reiten translatedirecting modulesregular componentindecomposable projective \(A\)-module\(DTr\)- orbitsindecomposable finitely generated right \(A\)-modulestrongly directing module

Mathematics Subject Classification ID

Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers (16G70) Representations of associative Artinian rings (16G10)

Related Items (10)

The Krull-Gabriel dimension of cycle-finite Artin algebras ⋮ Auslander–Reiten components with bounded short cycles ⋮ Cycle-finite algebras having finitely many indecomposable modules lying on short paths with injective source and projective target ⋮ A characterization of cycle-finite generalized double tilted algebras. ⋮ On algebras of generalized standard semiregular type ⋮ On the number of terms in the middle of almost split sequences over cycle-finite Artin algebras. ⋮ Algebras with cycle-finite Galois coverings ⋮ Finite cycles of indecomposable modules. ⋮ On Artin algebras with almost all indecomposable modules of projective or injective dimension at most one. ⋮ Cycle-Finite Module Categories

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