On subinjectivity domains of RD-injective modules

The subjectivity domain of a module allows us to evaluate how close (or far) a module is from being injective. In this paper, we consider three families of rings characterized by their RD-injective left [Formula: see text]-modules via the subinjective domain: those whose noninjective RD-injective left [Formula: see text]-modules are subinjective relatively only to divisible modules, those whose noninjective RD-injective left [Formula: see text]-modules are subinjective relatively only to fp-injective modules and those whose noninjective RD-injective left [Formula: see text]-modules are subinjective relatively only to injective modules.

A Study of The Density Property in Module Theory

In this paper, there are two main objectives. The first objective is to study the relationship between the density property and some modules in detail, for instance; semisimple and divisible modules. The Addition complement has a good relationship with the density property of the modules as this importance is highlighted by any submodule N of M has an addition complement with Rad(M)=0. The second objective is to clarify the relationship between the density property and the essential submodules with some examples. As an example of this relationship, we studied the torsion-free module and its relationship with the essential submodules in module M.

HW-DIVISIBLE MODULES

In this paper, we introduce a class of R- modules called hw-divisible modules and then we investigate some properties of them.