Chia Zargeh (2021)
Communications in Mathematics
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In this paper we introduce the notion of existentially closed Leibniz algebras. Then we use HNN-extensions of Leibniz algebras in order to prove an embedding theorem.
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.
J. Słomiński
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CONTENTSINTRODUCTION...................................................................................................................................................................... 31. TERMS NOTATION AND LEMMAS.................................................................................................................................. 4A. Quasi-algebras and algebras..........................................................................................................................................................................
Flávio U. Coelho, José A. de la Peña, Sonia Trepode (2008)
Colloquium Mathematicae
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A minimal non-tilted triangular algebra such that any proper semiconvex subcategory is tilted is called a tilt-semicritical algebra. We study the tilt-semicritical algebras which are quasitilted or one-point extensions of tilted algebras of tame hereditary type. We establish inductive procedures to decide whether or not a given strongly simply connected algebra is tilted.
Giorgia Bellomonte, Camillo Trapani (2013)
Studia Mathematica
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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...
Marta Kwiecień, Andrzej Skowroński (2009)
Colloquium Mathematicae
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In continuation of our article in Colloq. Math. 116.1, we give a complete description of the symmetric algebras of strictly canonical type by quivers and relations, using Brauer quivers.
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.
Kazimierz Głazek, Anzelm Iwanik (1974)
Colloquium Mathematicum
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König, Steffen, Xi, Changchang (1999)
Electronic Research Announcements of the American Mathematical Society [electronic only]
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K.R. Goodearl, D.E. Handelman (1982)
Journal für die reine und angewandte Mathematik
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Giorgia Bellomonte, Camillo Trapani (2011)
Studia Mathematica
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A generalized procedure for the construction of the inductive limit of a family of C*-algebras is proposed. The outcome is no more a C*-algebra but, under certain assumptions, a locally convex quasi *-algebra, named a C*-inductive quasi *-algebra. The properties of positive functionals and representations of C*-inductive quasi *-algebras are investigated, in close connection with the corresponding properties of positive functionals and representations of the C*-algebras that generate...
Camillo Trapani (2004)
Studia Mathematica
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Junping Liu, Changguo Wei (2014)
Czechoslovak Mathematical Journal
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In this paper, we consider the classification of unital extensions of -algebras by their six-term exact sequences in -theory. Using the classification theory of -algebras and the universal coefficient theorem for unital extensions, we give a complete characterization of isomorphisms between unital extensions of -algebras by stable Cuntz algebras. Moreover, we also prove a classification theorem for certain unital extensions of -algebras by stable purely infinite simple -algebras...
Flávio U. Coelho, Ma. I. R. Martins, Bertha Tomé (2004)
Colloquium Mathematicae
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We study the simple connectedness and strong simple connectedness of the following classes of algebras: (tame) coil enlargements of tame concealed algebras and n-iterated coil enlargement algebras.
Deng, Bangming, Xi, Changchang (1995)
Beiträge zur Algebra und Geometrie
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Antonio Fernández, M. Florencio, Pedro J. Paúl, Vladimir Müller (1989)
Collectanea Mathematica
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J.A. de de Pena (1988)
Manuscripta mathematica
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Andrzej Skowroński, Kunio Yamagata (2003)
Colloquium Mathematicae
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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.
Ibrahim Assem (2009)
Colloquium Mathematicae
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We define a notion of left section in an Auslander-Reiten component, by weakening one of the axioms for sections. We derive a generalisation of the Liu-Skowroński criterion for tilted algebras, then apply our results to describe the Auslander-Reiten components lying in the left part of an artin algebra.