In this study, the concept of m-projective modules is introduced. A right R-module M is said
to be m-projective if Ext (M, N)= 0 for any m-injective right R-module N. We prove that every …

Let R be a ring and 𝑆 be a class of some finitely generated left R-modules. Then a left R-
module M is called 𝑆-projective if for every homomorphism f: S→ M, where S∈ 𝑆, there exist …

In this paper we study M-small principally injective (in short, M-sp-injective) module which is
the generalization of M-principally injective module. We prove that if M is finite dimensional …

Let $ R $ be a ring and $ M $ a right $ R $-module with $ S= End_R (M) $. A module $ M $ is
called semi-projective if for any epimorphism $ f: M\rightarrow N $, where $ N $ is a …

In this paper, we introduce the notion of c-co-epi-retractable modules. An R-module M is
called c-co-epi-retractable if it contains a copy of its factor module by a complement …

Throughout this paper R represents commutative ring with identity, and M is a unitary left R-
module. The purpose of this paper is to study a new concept,(up to our knowledge), named …

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 is called pseudo-projective if every epimorphism from M to each quotient
module of M can be lifted to an endomorphism of M. In this paper, we study some properties …

Let R be a ring and M be an R-module. M is said to be an E-module (respectively, an EE-
module) if M has a supplement (respectively, ample supplements) in every coatomic …

Abstract A left R-module M is said to be fp-injective if, for every monomorphism K→ L with K
and L finitely presented left R-modules, Hom (L, M)→ Hom (K, M) is an epimorphism. A right …