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 …

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 …

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 …

If M and N are right R-modules, M is called simple-N-injective if every R-homomorphism γ
from a submodule K of N into M with γ (K) simple extends to N. In this paper, a right R …

A ring R is a right SI-ring if every singular right R-module is injective, while R is a right S3I-
ring if every singular semisimple right R-module is injective. In this paper, we investigate and …

In this paper, we introduce and study the pure-direct-projective modules, that is the modules
M every pure submodule A of which with M/A isomorphic to a direct summand of M is a direct …

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 left R-module M is said to be left singly injective if Ext R 1 (F/K, M)= 0 for any cyclic
submodule K of any finitely generated free left R-module F. In this paper, we study the notion …

We studied almost relative projective modules and almost relative injective modules in [3, 6,
7]. In this short note we define a new module, an almost projective (resp. almost injective) …

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 …