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.
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.
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.
R. Bautista, E. Pérez, L. Salmerón (2011)
Colloquium Mathematicae
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We continue the study of ditalgebras, an acronym for "differential tensor algebras", and of their categories of modules. We examine extension/restriction interactions between module categories over a ditalgebra and a proper subditalgebra. As an application, we prove a result on representations of finite-dimensional tame algebras Λ over an algebraically closed field, which gives information on the extension/restriction interaction between module categories of some special algebras Λ₀,...
R. M. Aquino, E. L. Green, E. N. Marcos (2002)
Colloquium Mathematicae
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Given a finite-dimensional algebra, we present sufficient conditions on the projective presentation of the algebra modulo its radical for a tilted algebra to be a Koszul algebra and for the endomorphism ring of a tilting module to be a quasi-Koszul algebra. One condition we impose is that the algebra has global dimension no greater than 2. One of the main techniques is studying maps between the direct summands of the tilting module. Some applications are given. We also show that a Brenner-Butler...
Zimmermann, Alexander (2003)
AMA. Algebra Montpellier Announcements [electronic only]
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Jerzy Nehring, Andrzej Skowroński (1989)
Fundamenta Mathematicae
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K. Erdmann, D. Madsen, V. Miemietz (2010)
Colloquium Mathematicae
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We consider functorially finite subcategories in module categories over Artin algebras. One main result provides a method, in the setup of bounded derived categories, to compute approximations and the end terms of relative Auslander-Reiten sequences. We also prove an Auslander-Reiten formula for the setting of functorially finite subcategories. Furthermore, we study the category of modules filtered by standard modules for certain quasi-hereditary algebras and we classify precisely when...
Stanisław Kasjan (1998)
Colloquium Mathematicae
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Hagen Meltzer (2001)
Colloquium Mathematicae
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Zbigniew Leszczyński, Andrzej Skowroński (2000)
Colloquium Mathematicae
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We describe all finite-dimensional algebras A over an algebraically closed field for which the algebra of 2×2 upper triangular matrices over A is of tame representation type. Moreover, the algebras A for which is of polynomial growth (respectively, domestic, of finite representation type) are also characterized.
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.
J. A. de la Peña (1990)
Banach Center Publications
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Piotr Malicki (1998)
Colloquium Mathematicae
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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.