An R-module F is called closed (neat) projective if, for every closed (neat) submodule L of
every R-module M, every homomorphism from F to M/L lifts to M. In this paper, we study …

In this paper, we prove that the Bass class with respect to a semidualizing bimodule C
contains all FP-injective S-modules. We introduce the definition of C-FP-injective modules …

In this article, several characterizations of certain classes of rings via FC-purity and I-purity
are considered. Among others results, it is shown that every I-pure injective left R-module is …

Let R be a ring. A right R-module A is said to be C-flat if the kernel of any epimorphism B→ A
is C-pure in B, ie the induced map Hom (C, B)→ Hom (C, A) is surjective for any cyclic right …

In this paper we study MC-pseudo injective module which is the generalization of pseudo
injective module and we give an example of MC-pseudo injective module which is not M …

ABSTRACT In a recent paper [3], a new approach in the study of the classical projectivity
was introduced. Subprojectivity domain of module was introduced as a tool to measure the …

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) …

Let R be a commutative ring, M be an R-module, and w be the so-called w-operation on R.
Set S w={f∈ R [X]| c (f) w= R}, where c (f) denotes the content of f. Let R {X}= R [X] S w and M …

Let C be a class of some finitely presented left R-modules. A left R-module M is called C-
injective, if Ext R 1 (C, M)= 0 for each C∈ C. A right R-module M is called C-flat, if Tor 1 R …

PM Cohn [3] has introduced the notion of purity for R-modules. With respect to purity, flat,
absolutely pure and regular modules are studied. In this paper we introduce and study the …