Marta Kwiecień, Andrzej Skowroński (2009)
Colloquium Mathematicae
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We develop the representation theory of selfinjective algebras of strictly canonical type and prove that their Auslander-Reiten quivers admit quasi-tubes maximally saturated by simple and projective modules.
J. Słomiński
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CONTENTSIntroduction.................................................................................................................... 5§ 1. Fundamental concepts for quasi-algebras..................................................... 5§ 2. Peano-algebras.................................................................................................... 13§ 3. Peano-algebras and free quasi-algebras....................................................... 25§ 4. Theorems concerning free...
König, Steffen, Xi, Changchang (1999)
Electronic Research Announcements of the American Mathematical Society [electronic only]
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Claus Michael Ringel (1990)
Banach Center Publications
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Giorgia Bellomonte, Camillo Trapani (2013)
Studia Mathematica
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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.
Kazimierz Głazek, Anzelm Iwanik (1974)
Colloquium Mathematicum
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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.
J. Słomiński
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CONTENTSINTRODUCTION...................................................................................................................................................................... 31. TERMS NOTATION AND LEMMAS.................................................................................................................................. 4A. Quasi-algebras and algebras..........................................................................................................................................................................
Deng, Bangming, Xi, Changchang (1995)
Beiträge zur Algebra und Geometrie
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Ibrahim Assem, Dan Zacharia (2003)
Colloquium Mathematicae
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Let A and R be two artin algebras such that R is a split extension of A by a nilpotent ideal. We prove that if R is quasi-tilted, or tame and tilted, then so is A. Moreover, generalizations of these properties, such as laura and shod, are also inherited. We also study the relationship between the tilting R-modules and the tilting A-modules.
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...
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.
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.
Generalov, A.I. (2002)
Zapiski Nauchnykh Seminarov POMI
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Jessica Lévesque (2003)
Colloquium Mathematicae
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We prove that a stably hereditary bound quiver algebra A = KQ/I is iterated tilted if and only if (Q,I) satisfies the clock condition, and that in this case it is of type~Q. Furthermore, A is tilted if and only if (Q,I) does not contain any double-zero.
Steffen König (1995)
Mathematische Zeitschrift
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Camillo Trapani (2004)
Studia Mathematica
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Lutz Hille, Dieter Vossieck (2003)
Colloquium Mathematicae
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Let Γ be a finite-dimensional hereditary basic algebra. We consider the radical rad Γ as a Γ-bimodule. It is known that there exists a quasi-hereditary algebra 𝓐 such that the category of matrices over rad Γ is equivalent to the category of Δ-filtered 𝓐-modules ℱ(𝓐,Δ). In this note we determine the quasi-hereditary algebra 𝓐 and prove certain properties of its module category.
Zygmunt Pogorzały, Mirosława Sufranek (2004)
Colloquium Mathematicae
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The class of n-fundamental algebras is introduced. It is a subclass of string algebras. For n-fundamental algebras we study the problem of when the Auslander-Reiten quiver contains, at the beginning or at the end, a component which is not generalized standard.