Using U-torsionless module we characterize U-neat submodules and Au-injective modules.
If M is a left R-module, U is E (M)-injective and Eu (M)/M does not contain a nonzero …

In this note we examine the 𝒯-torsion submodule of quasi-injective R-modules, R a ring with
unit, where 𝒯 is a torsion class in the sense of SE Dickson. We show that for a stable torsion …

We introduce and study a nontrivial generalization of uniserial modules and rings. A module
is called weakly uniserial if its submodules are comparable regarding embedding. Also, a …

Throughout this paper R is a ring with identity and every i?-module is unital. Let r be a
hereditary torsion theory with respect to R (see Golan [3]). A submodule N of a right i …

In this paper, we introduce the concept of NN-torsion-free modules (respectively, NN-
injective modules) as a generalization of nonnil-torsion-free modules (respectively, injective …

In this paper, we give some characterizations of modules M over a ring R such that every
submodule has a unique closure relative to a hereditary torsion theory on Mod-R by using …

By utilizing known characterizations of w-Noetherian rings in terms of injective modules, we
give more characterizations of w-Noetherian rings. More precisely, we show that a …

Let $ R $ be a Noetherian ring and let $ C $ be a semidualizing $ R $-module. In this paper,
we are concerned with the tensor and torsion product of $ C $-injective modules. Firstly, it is …

An R-module M is said to be an extending module if every closed submodule of M is a direct
summand. In this paper we introduce and investigate the concept of a type 2 τ-extending …

A submodule N of a module M is called S-closed (in M) if M/N is nonsingular. It is well-known
that the class Closed of short exact sequences determined by closed submodules is a …