Prescribing endomorphism algebras. The cotorsion-free case
Primary decomposition of torsion -modules.
Products of small modules
Module is said to be small if it is not a union of strictly increasing infinite countable chain of submodules. We show that the class of all small modules over self-injective purely infinite ring is closed under direct products whenever there exists no strongly inaccessible cardinal.
Projectivity and flatness over the colour endomorphism ring of a finitely generated graded comodule.
Projectivity and flatness over the endomorphism ring of a finitely generated comodule.
Projectivity and flatness over the endomorphism ring of a finitely generated module.
Quotient rings and one-sided primes.
Reduced p.p.-rings without identity.
Reduction Theorems for Endomorphism Near-Rings.
Rings whose modules are finitely generated over their endomorphism rings
A module M is called finendo (cofinendo) if M is finitely generated (respectively, finitely cogenerated) over its endomorphism ring. It is proved that if R is any hereditary ring, then the following conditions are equivalent: (a) Every right R-module is finendo; (b) Every left R-module is cofinendo; (c) R is left pure semisimple and every finitely generated indecomposable left R-module is cofinendo; (d) R is left pure semisimple and every finitely generated indecomposable left R-module is finendo;...
Rota-type operators on 3-dimensional nilpotent associative algebras
We give the description of Rota–Baxter operators, Reynolds operators, Nijenhuis operators and average operators on 3-dimensional nilpotent associative algebras over .
Semicommutativity of the rings relative to prime radical
In this paper, we introduce a new kind of rings that behave like semicommutative rings, but satisfy yet more known results. This kind of rings is called -semicommutative. We prove that a ring is -semicommutative if and only if is -semicommutative if and only if is -semicommutative. Also, if is -semicommutative, then is -semicommutative. The converse holds provided that is nilpotent and is power serieswise Armendariz. For each positive integer , is -semicommutative if and...
Skeletons, bodies and generalized -algebras
Small almost free modules with prescribed topological endomorphism rings
Sobre anillos de polinomios que son anillos de Bézout.
Solvable Normal Subgroups and Nilpotent Ideals in Matrix Rings.
Some constructions related to Rees matrix rings.
Some external characterizations of SV-rings and hereditary rings.
Strong stably finite rings and some extensions.
Strongly regular rings.