On a class of tame symmetric algebras having only periodic modules
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Displaying 1 – 20 of 23
On artin algebras with almost all indecomposable modules of projective or injective dimension at most one
Andrzej Skowroński (2003)
Open Mathematics
Let A be an artin algebra over a commutative artin ring R and ind A the category of indecomposable finitely generated right A-modules. Denote to be the full subcategory of ind A formed by the modules X whose all predecessors in ind A have projective dimension at most one, and by the full subcategory of ind A formed by the modules X whose all successors in ind A have injective dimension at most one. Recently, two classes of artin algebras A with co-finite in ind A, quasi-tilted algebras and...
On Auslander-Reiten translates in functorially finite subcategories and applications
K. Erdmann, D. Madsen, V. Miemietz (2010)
Colloquium Mathematicae
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 this category...
On hereditary artinian rings and the pure semisimplicity conjecture: rigid tilting modules and a weak conjecture
José L. García (2014)
Colloquium Mathematicae
A weak form of the pure semisimplicity conjecture is introduced and characterized through properties of matrices over division rings. The step from this weak conjecture to the full pure semisimplicity conjecture would be covered by proving that there do not exist counterexamples to the conjecture in a particular class of rings, which is also studied.
On hereditary rings and the pure semisimplicity conjecture II: Sporadic potential counterexamples
José L. García (2015)
Colloquium Mathematicae
It was shown in [Colloq. Math. 135 (2014), 227-262] that the pure semisimplicity conjecture (briefly, pssC) can be split into two parts: first, a weak pssC that can be seen as a purely linear algebra condition, related to an embedding of division rings and properties of matrices over those rings; the second part is the assertion that the class of left pure semisimple sporadic rings (ibid.) is empty. In the present article, we characterize the class of left pure semisimple sporadic rings having finitely...
On locally bounded categories stably equivalent to the repetitive algebras of tubular algebras
Zygmunt Pogorzały (1997)
Colloquium Mathematicae
On perpendicular categories of stones over quiver algebras.
D. Happel, S. Hartlieb, O. Kerner (1996)
Commentarii mathematici Helvetici
On pure semisimplicity and representation-finite piecewise prime rings
Bogumiła Klemp, Daniel Simson (1990)
Banach Center Publications
On restrictions of generic modules of tame algebras
Raymundo Bautista, Efrén Pérez, Leonardo Salmerón (2013)
Open Mathematics
Given a convex algebra ∧0 in the tame finite-dimensional basic algebra ∧, over an algebraically closed field, we describe a special type of restriction of the generic ∧-modules.
On self-injective algebras of finite representation type
Marta Błaszkiewicz, Andrzej Skowroński (2012)
Colloquium Mathematicae
We describe the structure of finite-dimensional self-injective algebras of finite representation type over a field whose stable Auslander-Reiten quiver has a sectional module not lying on a short chain.
On selfinjective algebras of tilted type
Andrzej Skowroński, Kunio Yamagata (2015)
Colloquium Mathematicae
We provide a characterization of all finite-dimensional selfinjective algebras over a field K which are socle equivalent to a prominent class of selfinjective algebras of tilted type.
On selfinjective algebras without short cycles in the component quiver
Maciej Karpicz (2011)
Colloquium Mathematicae
We give a complete description of all finite-dimensional selfinjective algebras over an algebraically closed field whose component quiver has no short cycles.
On selfinjective artin algebras having nonperiodic generalized standard Auslander-Reiten components
Andrzej Skowroński, Kunio Yamagata (2003)
Colloquium Mathematicae
We describe the structure of all selfinjective artin algebras having at least three nonperiodic generalized standard Auslander-Reiten components. In particular, all selfinjective artin algebras having a generalized standard Auslander-Reiten component of Euclidean type are described.
On split-by-nilpotent extensions
Ibrahim Assem, Dan Zacharia (2003)
Colloquium Mathematicae
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.
On the Auslander-Reiten valued quiver of right peak rings
Bogumiła Klemp, Daniel Simson (1990)
Fundamenta Mathematicae
On the category of modules of second kind for Galois coverings
Piotr Dowbor (1996)
Fundamenta Mathematicae
Let F: R → R/G be a Galois covering and (resp. ) be a full subcategory of the module category mod (R/G), consisting of all R/G-modules of first (resp. second) kind with respect to F. The structure of the categories and is given in terms of representation categories of stabilizers of weakly-G-periodic modules for some class of coverings.
On the existence of almost split sequences in subcategories
Raymundo Bautista, Mark Kleiner (1990)
Banach Center Publications
On the Freyd categories of an additive category.
Beligiannis, Apostolos (2000)
Homology, Homotopy and Applications
On the lattice of cotilting modules.
Buan, Aslak Bakke, Krause, Henning, Solberg, Øyvind (2002)
AMA. Algebra Montpellier Announcements [electronic only]
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
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.
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