Let be a non-empty collection of right ideals of a ring R. A right R-module X is called-
injective provided each R-homomorphism ϕ: A→ X with A in can be lifted to an R …

In this paper, we introduce the notion of abelian endoregular modules as those modules
whose endomorphism rings are abelian von Neumann regular. We characterize an abelian …

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

It is well-known that a ring R is right Noetherian if and only if every direct sum of injective
right R-modules is injective. In this paper, we characterize Nonnil-Noetherian rings by …

A submodule A of a left module B (over an associative ring with 1) is pure if for any right
module F, the natural homomorphism F⊗ A→ F⊗ B is injective. A module C is pure-injective …

An R-module M is called principally quasi-injective if each R-hornomorphism from a
principal submodule of M to M can be extended to an endomorphism of M. Many properties …

It is proved that A is a right distributive ring if and only if all quasiinjective right A-modules are
Bezout left modules over their endomorphism rings if and only if for any quasiinjective right A …

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 introduce T-noncosingular modules. Rings for which all right modules are T-
noncosingular are shown to be precisely those for which every simple right module is …

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 …