Close CSL algebras are similar.
David R. Pitts (1994)
Mathematische Annalen
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David R. Pitts (1994)
Mathematische Annalen
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Ulrich Stegmeir (1979)
Mathematische Annalen
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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...
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.
Sung Sa Hong, Louis D. Nel (1979)
Mathematische Zeitschrift
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Grzegorz Bobiński, Piotr Malicki (2008)
Colloquium Mathematicae
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We classify, up to derived (equivalently, tilting-cotilting) equivalence, all nondegenerate gentle two-cycle algebras. We also give a partial classification and formulate a conjecture in the degenerate case.
Maciej Karpicz (2011)
Colloquium Mathematicae
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We give a complete description of all finite-dimensional selfinjective algebras over an algebraically closed field whose component quiver has no short cycles.
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,...
Jaroslav Ježek (1974)
Colloquium Mathematicae
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Generalov, A.I. (2002)
Zapiski Nauchnykh Seminarov POMI
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Seidon Alsaody (2011)
Colloquium Mathematicae
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This is a study of morphisms in the category of finite-dimensional absolute valued algebras whose codomains have dimension four. We begin by citing and transferring a classification of an equivalent category. Thereafter, we give a complete description of morphisms from one-dimensional algebras, partly via solutions of real polynomials, and a complete, explicit description of morphisms from two-dimensional algebras. We then give an account of the reducibility of the morphisms, and for...
Claude Cibils (1991)
Mathematische Annalen
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Šlapal, Josef (1996)
Mathematica Pannonica
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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.
Alicja Jaworska-Pastuszak, Andrzej Skowroński (2013)
Colloquium Mathematicae
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We describe the structure of finite-dimensional algebras of domestic representation type over an algebraically closed field whose Auslander-Reiten quiver consists of generalized standard and semiregular components. Moreover, we prove that this class of algebras contains all special biserial algebras whose Auslander-Reiten quiver consists of semiregular components.
M. Barot, O. Mendoza (2006)
Colloquium Mathematicae
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An easy explicit construction is given for a full and faithful functor from the bounded derived category of modules over an associative algebra A to the stable category of the repetitive algebra of A. This construction simplifies the one given by Happel.
Keller, Bernhard (2001)
Homology, Homotopy and Applications
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T.W. Gamelin (1978)
Mathematische Annalen
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