Degenerations for indecomposable modules and tame algebras
Andrzej Skowroński, Grzegorz Zwara (1998)
Annales scientifiques de l'École Normale Supérieure
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Displaying similar documents to “On nonexistence of oriented cycles in Auslander-Reiten quivers”
Degenerations for indecomposable modules and tame algebras
On the number of terms in the middle of almost split sequences over cycle-finite artin algebras
Piotr Malicki, José Peña, Andrzej Skowroński (2014)
Open Mathematics
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We prove that the number of terms in the middle of an almost split sequence in the module category of a cycle-finite artin algebra is bounded by 5.
On the structure of indecomposable modules over Artin algebras
Andrzej Skowroński (1984)
Colloquium Mathematicae
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Directing components for quasitilted algebras
Flávio Coelho (1999)
Colloquium Mathematicae
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We show here that a directing component of the Auslander-Reiten quiver of a quasitilted algebra is either postprojective or preinjective or a connecting component.
Domestic iterated one-point extensions of algebras by two-ray modules
Grzegorz Bobiński, Andrzej Skowroński (2003)
Open Mathematics
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In the paper, we introduce a wide class of domestic finite dimensional algebras over an algebraically closed field which are obtained from the hereditary algebras of Euclidean type , n≥1, by iterated one-point extensions by two-ray modules. We prove that these algebras are domestic and their Auslander-Reiten quivers admit infinitely many nonperiodic connected components with infinitely many orbits with respect to the action of the Auslander-Reiten translation. Moreover, we exhibit a...
A note on tilting sequences
Clezio Braga, Flávio Coelho (2008)
Open Mathematics
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We discuss the existence of tilting modules which are direct limits of finitely generated tilting modules over tilted algebras.
Degenerations for representations of tame quivers
Klaus Bongartz (1995)
Annales scientifiques de l'École Normale Supérieure
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A characterization of representation-finite algebras
Andrzej Skowroński, M. Wenderlich (1991)
Fundamenta Mathematicae
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Let A be a finite-dimensional, basic, connected algebra over an algebraically closed field. Denote by Γ(A) the Auslander-Reiten quiver of A. We show that A is representation-finite if and only if Γ(A) has at most finitely many vertices lying on oriented cycles and finitely many orbits with respect to the action of the Auslander-Reiten translation.
Cycle-finite algebras with almost all indecomposable modules of projective or injective dimension at most one
Adam Skowyrski (2013)
Colloquium Mathematicae
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We describe the structure of artin algebras for which all cycles of indecomposable modules are finite and almost all indecomposable modules have projective or injective dimension at most one.