On nonexistence of oriented cycles in Auslander-Reiten quivers
On non-Spechtianness of the variety of associative rings that satisfy the identity .
On nonstandard tame selfinjective algebras having only periodic modules
We investigate degenerations and derived equivalences of tame selfinjective algebras having no simply connected Galois coverings but the stable Auslander-Reiten quiver consisting only of tubes, discovered recently in [4].
On one class of purities
On Order and Topological Completeness.
On ordered division rings
Prestel introduced a generalization of the notion of an ordering of a field, which is called a semiordering. Prestel's axioms for a semiordered field differ from the usual (Artin-Schreier) postulates in requiring only the closedness of the domain of positivity under x ↦ xa² for non-zero a, in place of requiring that positive elements have a positive product. Our aim in this work is to study this type of ordering in the case of a division ring. We show that it actually behaves just as in the commutative...
On ordered division rings
Prestel introduced a generalization of the notion of an ordering of a field, which is called a semiordering. Prestel’s axioms for a semiordered field differ from the usual (Artin-Schreier) postulates in requiring only the closedness of the domain of positivity under for nonzero , instead of requiring that positive elements have a positive product. In this work, this type of ordering is studied in the case of a division ring. It is shown that it actually behaves the same as in the commutative...
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 pairs of subrings with a common set of proper ideals.
On path coalgebras of quivers with relations
The notion of the path coalgebra of a quiver with relations introduced in [11] and [12] is studied. In particular, developing this topic in the context of the weak* topology, we give a criterion that allows us to verify whether or not a relation subcoalgebra of a path coalgebra is the path coalgebra of a quiver with relations.
On periodic rings.
On perpendicular categories of stones over quiver algebras.
On P-extending modules.
On p.p.-rings which are reduced.
On presentations of semigroup rings
Siano un ideale di un anello e una congruenza su un semigruppo . Consideriamo l'anello semigruppo come un'immagine omomorfa dell'anello semigruppo . Questo è fatto in tre passi: prima studiando l'anello semigruppo , poi e infine combinando i due casi speciali. In ciascun caso, determiniamo l'ideale che è il nucleo dell'omomorfismo in questione. I risultati corrispondenti per le -algebre, dove è un anello commutativo, possono essere facilmente dedotti. Alcuni raffinamenti, casi speciali...
On presented dimensions of modules and rings.
On primary and reduced varieties of monoassociative algebras.
On prime and semiprime near-rings with derivations.
On Prime Ideals in Representation Rings.