Let M and N be two modules. M is called automorphism N-invariant if for any essential
submodule A of N, any essential monomorphism f: A→ M can be extended to some g∈ Hom …

In this article, we focus on modules M such that every homomorphism from a projection
invariant submodule of M to M can be lifted to M. Although such modules share some of the …

A module $ M $ is called ECS if every ec-closed submodule of $ M $ is a direct summand. It
was shown that the ECS property lies strictly between CS and P-extending properties. We …

This paper is a continuation of study semi-potentness endomorphism rings of module. We
give some other characterizations of endomorphism ring to be semi-potent. New results are …

Let R be a ring. In this note we study some properties of principally quasi-injective strongly
Kasch R-modules and show that if MR is a principally quasi-injective strongly Kasch module …

In this paper, we study the notions (strongly) soc-injective,(strongly) simple-injective and
(strongly) mininjective modules in σ [M]. For any module N in σ [M], N is strongly mininjective …

Let M be a right R-module. It is shown that M is a locally Noetherian module if every finitely
generated module in σ [M] is a direct sum of a projective module and a CS-module …

In this work, injective semimodule has been generalized to almost-injective semimodule.
The aim of this research is to study the basic properties of the concept almost-injective …

In this paper certain injectivity conditions in terms of extensions of monomorphisms are
considered for submodules. More precisely we studied properties and characterizations of …

In this thesis, we will study the relations between weakly injective, weakly projective versus
extending and lifting modules and its generalization. Mainly, we study rings over which …