We say that an R-module M is virtually semisimple if each submodule of M is isomorphic to a
direct summand of M. A nonzero indecomposable virtually semisimple module is then called …

Abstract A right R-module M is virtually extending (or CIS) if every complement submodule of
M is isomorphic to a direct summand of M, and M is called a virtually C2-module if every …

Abstract In 2016, Facchini and Nazemian defined the notion of iso-Artinian and iso-
Noetherian modules and rings. We discuss some new properties of iso-Artinian and iso …

This paper describes properties of three certain classes of modules M over a ring R
determined by conditions on isomorphic direct summands (≲⊕): The condition that …

Modules in which every submodule is isomorphic to a direct summand is called virtually
semisimple. In this article, we carry out a study of virtually semisimple modules over a …

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 …

We study the class of virtually uniserial modules and rings as a nontrivial generalization of
uniserial modules and rings. An R-module M is virtually uniserial if for every finitely …

In the past few decades, researchers have found that studying modules using
endomorphisms is a powerful and useful tool. This has led to valuable works in this field …

The main aim of the paper is to describe the structure of modules and corresponding rings
satisfying the property (P), which says that M/im (α) is embeddable into ker⁡(α) for each …

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 …