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 …

A module M over a ring is called simple-direct-injective if, whenever A and B are simple
submodules of M with A≅ B and B⊆⊕ M, we have A⊆⊕ M. Various basic properties of …

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 …

In this paper, we characterize strongly right C 2-rings in terms of finite-direct-injective
modules which is a generalization of direct-injective modules (or C 2-modules). Using this …

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 …

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 …

In this paper, we study the class of modules having the property that if any pure submodule
is isomorphic to a direct summand of such a module then the pure submodule is itself a …

ABSTRACT A right R-module M is called simple-direct-injective if, whenever, A and B are
simple submodules of M with A≅ B, and B⊆⊕ M, then A⊆⊕ M. Dually, M is called simple …

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 …

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 …