A ring R is called a V-ring, respectively SSI-ring, respectively QII-ring if simple, respectively
semisimple, respectively quasi-injective, right R-modules are injective. We show that R is …

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 …

Kaplansky [11] noticed that a commutative ring is (von Neumann) regular if and only if it is a
V-ring, that is, each simple module over the ring is injective. However in the general case …

In recent years, von Neumann regular rings and V-rings have been extensively studied
(cf.[3J,[4J,[9J,[10],[11]). P-injectivity and pV-rings (which generalize regular rings and V …

The concept of weak relative-injectivity of modules was introduced originally in [10], where it
is shown that a semiperfect ring R is such that every cyclic right module is embeddable …

It will be shown that a particular quotient ring of a ring $ R $ is a nontrivial $ V $-ring if $ R $
is a special kind of a right hereditary, right Noetherian ring. Another result states that all …

Let R be a ring. JS-injective right R-modules are introduced and studied in this paper as a
generalization of small-injective right R-modules. Let N and M be right R-modules. A module …

In this paper, we investigate some properties of rings whose simple (singular) right R−
modules are AP-injective. It is proved that an MERT ring R is von Neumann regular if and …

Recently, the rings whose injective right modules are R-projective (respectively, max-
projective) were investigated and studied in [2]. Such ring are called right almost-QF …

Let R be a ring and M be an R-module. In this paper we investigate modules M such that
every (simple) cosingular R-module is M-projective. We prove that every simple cosingular …