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A general form of non-Frobenius self-injective algebras

Andrzej Skowroński, Kunio Yamagata (2006)

Colloquium Mathematicae

Applying the classical work of Nakayama [Ann. of Math. 40 (1939)], we exhibit a general form of non-Frobenius self-injective finite-dimensional algebras over a field.

Addendum to Zip rings.

Carl Faith (1992)

Publicacions Matemàtiques

We list some typos and minor correction that in no way affect the main results of Rings with zero intersection property on annihilators: Zip rings (Publicacions Matemàtiques 33, 2 (1989), pp. 329-338), e.g., nothing stated in the abstract is affected.

Algebras stably equivalent to trivial extensions of hereditary algebras of type à n

Zygmunt Pogorzały (1993)

Colloquium Mathematicae

The study of stable equivalences of finite-dimensional algebras over an algebraically closed field seems to be far from satisfactory results. The importance of problems concerning stable equivalences grew up when derived categories appeared in representation theory of finite-dimensional algebras [8]. The Tachikawa-Wakamatsu result [17] also reveals the importance of these problems in the study of tilting equivalent algebras (compare with [1]). In fact, the result says that if A and B are tilting...

Frobenius n-group algebras

Biljana Zeković (2002)

Discussiones Mathematicae - General Algebra and Applications

Frobenius algebras play an important role in the representation theory of finite groups. In the present work, we investigate the (quasi) Frobenius property of n-group algebras. Using the (quasi-) Frobenius property of ring, we can obtain some information about constructions of module category over this ring ([2], p. 66-67).

Full matrix algebras with structure systems

Hisaaki Fujita (2003)

Colloquium Mathematicae

We study associative, basic n × n𝔸-full matrix algebras over a field, whose multiplications are determined by structure systems 𝔸, that is, n-tuples of n × n matrices with certain properties.

Loewy coincident algebra and Q F -3 associated graded algebra

Hiroyuki Tachikawa (2009)

Czechoslovak Mathematical Journal

We prove that an associated graded algebra R G of a finite dimensional algebra R is Q F (= selfinjective) if and only if R is Q F and Loewy coincident. Here R is said to be Loewy coincident if, for every primitive idempotent e , the upper Loewy series and the lower Loewy series of R e and e R coincide. Q F -3 algebras are an important generalization of Q F algebras; note that Auslander algebras form a special class of these algebras. We prove that for a Loewy coincident algebra R , the associated graded algebra...

Morita duality for Grothendieck categories.

José L. Gómez Pardo, Francisco de A. Guil Asensio (1992)

Publicacions Matemàtiques

We survey some recent results on the theory of Morita duality for Grothendieck categories, comparing two different versions of this concept, and giving applications to QF-3 and Qf-3' rings.

On generalization of injectivity

Roger Yue Chi Ming (1992)

Archivum Mathematicum

Characterizations of quasi-continuous modules and continuous modules are given. A non-trivial generalization of injectivity (distinct from p -injectivity) is considered.

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