In this paper, we introduce and study the dual notion of simple-direct-injective modules.
Namely, a right R-module M is called simple-direct-projective if, whenever A and B are …

We investigate the strongly regularity of rings whose simple singular right R-modules are YJ-
injective. It is proved that the following conditions are equivalent for a ring R:(1) R is a …

Proper classes (or exact structures) offer rich research topics due to their important role in
category theory. Motivated by the studies on opposite of injective modules, we introduce a …

A module M is called a simple continuous module if it satisfies the conditions (min-C_1) and
(min-C_2). A module M is called singular simple-direct-injective if for any singular simple …

In this note, we find similar characteristic properties in terms of certain intersections of
maximal left ideals for the following classes of rings:(1) Left V-rings;(2) Left fV-rings;(3) Left …

In a series of recent papers, Beidar, Jain and Srivastava studied the question as to when a
ring R with the property that essential extensions of semi-simple right R-modules are direct …

Every indecomposable module over a generalized uniserial ring is uniserial, hence local.
This motivates one to study rings R satisfying the condition (*): R is a right artinian ring such …

Let R be a ring. A right R-module M is called minimal quasi-injective if every homomorphism
from a simple submodule of M to M can be extended to an endomorphism of M. Some …

Regular, right self-injective rings are considered. We settle the question of when such a ring
is a right V-ring, ie, when each simple right module over the ring is injective. It is proved that …

A right module M is called Wnil-injective if for any 0 ¹ a Î N (R), there exists a positive integer
n such that an ¹ 0 and any right R-homomorphism f: an R® M can be extended to R® M. In …