F-semiperfeke und perfekte Moduln in ... [M].
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.
Green walks in a hypergraph
Group representations without groups.
Growth and Lie brackets in the homotopy Lie algebra.
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.
Noncommutative Valuation Rings
Non-perfect rings and a theorem of Eklof and Shelah
We prove a stronger form, , of a consistency result, , due to Eklof and Shelah. concerns extension properties of modules over non-left perfect rings. We also show (in ZFC) that does not hold for left perfect rings.
On certain classes of modules.
Let X be a class or R-modules containing 0 and closed under isomorphic images. With any such X we associate three classes ΓX, FX and ΔX. The study of some of the closure properties of these classes allows us to obtain characterization of Artinian modules dualizing results of Chatters. The theory of Dual Glodie dimension as developed by the author in some of his earlier work plays a crucial role in the present paper.
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.
On local QF rings.
On Multiplicative Bases in Quasi Frobenius Algebras.
On orders in rQF-2 rings.
On -injectivity, YJ-injectivity and quasi-Frobeniusean rings
A new characteristic property of von Neumann regular rings is proposed in terms of annihilators of elements. An ELT fully idempotent ring is a regular ring whose simple left (or right) modules are either injective or projective. Artinian rings are characterized in terms of Noetherian rings. Strongly regular rings and rings whose two-sided ideals are generated by central idempotents are characterized in terms of special annihilators. Quasi-Frobeniusean rings are characterized in terms of -injectivity....
On Projective Resolutions of Frobenius Algebras and Gorenstein Rings.
On Regular Rings and Self-injective Rings, iv