On some additive mappings in rings with involution.
On some classes of modules
The aim of this paper is to investigate quasi-corational, comonoform, copolyform and -(co)atomic modules. It is proved that for an ordinal a right -module is -atomic if and only if it is -coatomic. And it is also shown that an -atomic module is quasi-projective if and only if is quasi-corationally complete. Some other results are developed.
On some commutativity theorems for finite rings and finite groups
On some equations related to derivations in rings.
On some formulas in the Hall algebra of the Kronecker algebra.
On some properties of -supplemented modules.
On some Radicals in Near-rings with a Defect of Distributivity
On some Results Related to Köthe's Conjecture
The Köthe conjecture states that if a ring R has no nonzero nil ideals then R has no nonzero nil one-sided ideals. Although for more than 70 years significant progress has been made, it is still open in general. In this paper we survey some results related to the Köthe conjecture as well as some equivalent problems.
On some weakly supernilpotent radicals of rings
On special Qr-filters of semigroups, semirings and rings.
On split-by-nilpotent extensions
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.
On splitting of extensions of rings and topological rings.
On Splitting Rings for Azumaya Skew Group Rings
On stable equivalences of module subcategories over a semiperfect noetherian ring
Given a semiperfect two-sided noetherian ring Λ, we study two subcategories and of the category mod Λ of finitely generated right Λ-modules, where Tr M is Auslander’s transpose of M. In particular, we give another convenient description of the categories and , and we study category equivalences and stable equivalences between them. Several results proved in [J. Algebra 301 (2006), 748-780] are extended to the case when Λ is a two-sided noetherian semiperfect ring.
On stable K-theory and topological Hochschild homology.
On strong commutativity-preserving maps.
On strongly 0-prime ideals in near-rings.
On strongly prime semiring.
On structure of certain periodic rings and near-rings.
On structure space of -semigroups
In this paper we introduce the notion of the structure space of -semigroups formed by the class of uniformly strongly prime ideals. We also study separation axioms and compactness property in this structure space.