A general form of non-Frobenius self-injective algebras
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.
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.
Addendum zu: Quasi-Frobenius-Algebren und lokal vollständige Durchschnitte:
Algebras stably equivalent to trivial extensions of hereditary algebras of type
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...
Algebren, Darstellungsköcher, Ueberlagerungen und zurück.
An action-free characterization of weak Hopf-Galois extensions.
An approach to Hopf algebras via Frobenius coordinates.
Character modules, submodules of a free module, and quasi-Frobenius rings.
Duality Theorem of Character Modules for Rings with Minimum Condition.
Exact sequences of pairs in commutative rings
FP-injective and weakly quasi-Frobenius rings.
Frobenius n-group algebras
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
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.
Group representations without groups.
Ikeda-Nakayama modules.
Isobaric QF-rings
Loewy coincident algebra and -3 associated graded algebra
We prove that an associated graded algebra of a finite dimensional algebra is (= selfinjective) if and only if is and Loewy coincident. Here is said to be Loewy coincident if, for every primitive idempotent , the upper Loewy series and the lower Loewy series of and coincide. -3 algebras are an important generalization of algebras; note that Auslander algebras form a special class of these algebras. We prove that for a Loewy coincident algebra , the associated graded algebra...
Morita duality for Grothendieck categories.
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
Characterizations of quasi-continuous modules and continuous modules are given. A non-trivial generalization of injectivity (distinct from -injectivity) is considered.
On generalizations of injectivity.