Short Chains and Short Cycles of Modules

DOI10.2307/2159166zbMath0794.16013OpenAlexW4231823605MaRDI QIDQ4038366

Idun Reiten, Sverre O. Smalø, Andrzej Skowroński

Publication date: 16 May 1993

Full work available at URL: https://doi.org/10.2307/2159166

zbMATH Keywords

Artin algebrastilted algebrasalgebras of finite representation typesincere indecomposable modulesmiddle of short chains

Mathematics Subject Classification ID

Module categories in associative algebras (16D90) Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers (16G70) Representations of associative Artinian rings (16G10) Homological dimension in associative algebras (16E10)

Related Items

Short Chains and Regular Components, Self-injective Artin algebras without short cycles in the component quiver., Selfinjective algebras without short cycles of indecomposable modules, Some Hall polynomials for representation-finite selfinjective algebra with \(\text{mod}_p\Lambda\) without short chains, On indecomposable modules without selfextensions, Auslander–Reiten components with bounded short cycles, Universal PBW-bases of Hall-Ringel algebras and Hall polynomials, Degenerations for modules over representation-finite biserial algebras, 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., Tilted algebras and short chains of modules., On selfinjective Artin algebras having generalized standard quasitubes., Hall polynomials and composition algebra of representation finite algebras, Module Categories Without Short Cycles Are of Finite Type, Tilted algebras and generalized standard Auslander-Reiten components, Finite cycles of indecomposable modules., Cycle-finite modules over artin algebras, Socle deformations of selfinjective orbit algebras of tilted type, Auslander-Reiten components determined by their composition factors, Sincere stable tubes, On $\Delta $–good module categories without short cycles

Cites Work

• Modules determined by their composition factors
• Tame algebras and integral quadratic forms
• Nonexistent cycles
• On a result of bautista and smal⊘ on cycles
• Modules with the same socles and tops as a directing module are isomorphic
• Some characterizations of tilted algebras.