A restricted artinian ring is a commutative ring with an identity in which every proper
homomorphic image is artinian. Cohen proved that a commutative ring R is restricted …

Inspired by the notion of virtually extending module, in this work we have proposed and
investigated the behaviours of virtually lifting module as the dual of virtually extending …

We call a right module $ M $(strongly) virtually regular if every (finitely generated) cyclic
submodule is isomorphic to a direct summand. $ M $ is said to be completely virtually …

In this paper, we study the Baer–Kaplansky theorem for injective modules. Firstly, we prove
that every right semi-artinian local ring satisfies the Baer–Kaplansky theorem for injective …

Noetherian rings have played a fundamental role in commutative algebra, algebraic number
theory, and algebraic geometry. Along with their dual, Artinian rings, they have many …

This article is a sequel to the recent three papers on “virtually semisimple modules and
rings,” by Behboodi et al., which two of them appeared in the Algebras and Representation …

This paper is a continuation of our previous article (Behbood and Bigdeli in Commun
Algebra 47: 3995–4008, 2019). We study commutative rings R whose proper (prime) ideals …

In this thesis, we characterize semisimple modules over noncommutative rings and
investigate their properties. We discuss noncommutative rings and their modules based on …