We introduce the class of “right almost V-rings” which is properly between the classes of
right V-rings and right good rings. A ring R is called a right almost V-ring if every simple R …

A ring R is called a right weakly V-ring (briefly, a right WV-ring) if every simple right R-
module is X-injective, where X is any cyclic right R-module with XR≇ RR. In this note, we …

Let R be a ring and be a class of right R-modules which is closed under submodules,
quotients and isomorphisms. A right R-module M is called-injective if for every T. A ring R is …

In this paper, we study rings with the property that every cyclic module is almost-injective
(CAI). It is shown that R is an Artinian serial ring with J (R)^ 2= 0 J (R) 2= 0 if and only if R is …

Right ue-rings (rings with the property of the title, ie, with the maximality of the right socle)
are investigated. It is shown that a semiprime ring R is a right ue-ring if and only if R is a …

A ring A is a completely integrally closed right A-module if and only if the maximal right ring
of quotients Q max (A) of A is an injective right A-module and A is a right completely …

A right $ R $-module $ M $ is called $ R $-projective provided that it is projective relative to
the right $ R $-module $ R_ {R} $. This paper deals with the rings whose all nonsingular …

In this paper, we extend some results of V rings to GP-V rings and GP-V'rings. Some
characterizations of strongly regular rings are obtained. We show that (1) R is strongly …

The notion of simple-direct-injective modules which are a generalization of injective
modules unifies $ C2 $ and $ C3 $-modules. In the present paper, we introduce the notion of …

It is well-known that a ring R is right PF if and only if it is semiperfect and right self-injective
with essential right socle. In this note, it is shown that a ring R is right PF if and only if u. dim …