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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.
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.
Marta Kwiecień, Andrzej Skowroński (2005)
Colloquium Mathematicae
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We give necessary and sufficient conditions for a wing of an Auslander-Reiten quiver of a selfinjective algebra to be the wing of the radical of an indecomposable projective module. Moreover, a characterization of indecomposable Nakayama algebras of Loewy length ≥ 3 is obtained.
Andrzej Skowroński, Adam Skowyrski (2014)
Colloquium Mathematicae
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We provide a characterization of artin algebras without chains of nonzero homomorphisms between indecomposable finitely generated modules starting with an injective module and ending with a projective module.
Claus Michael Ringel (1990)
Banach Center Publications
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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.
Andrzej Skowronski (1984)
Acta Universitatis Carolinae. Mathematica et Physica
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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...
Hagen Meltzer (2001)
Colloquium Mathematicae
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Andrzej Skowroński, Grzegorz Zwara (1998)
Annales scientifiques de l'École Normale Supérieure
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Zimmermann, Alexander (2003)
AMA. Algebra Montpellier Announcements [electronic only]
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Jerzy Białkowski, Andrzej Skowroński, Adam Skowyrski, Paweł Wiśniewski (2012)
Colloquium Mathematicae
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We describe the structure of artin algebras for which all cycles of indecomposable finitely generated modules are finite and all Auslander-Reiten components are semiregular.
Bertha Tomé (1995)
Fundamenta Mathematicae
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Let Λ be a finite-dimensional, basic and connected algebra over an algebraically closed field, and mod Λ be the category of finitely generated right Λ-modules. We say that Λ has acceptable projectives if the indecomposable projective Λ-modules lie either in a preprojective component without injective modules or in a standard coil, and the standard coils containing projectives are ordered. We prove that for such an algebra Λ the following conditions are equivalent: (a) Λ is tame, (b)...