A module satisfying the descending chain condition on cyclic submodules is called
coperfect. The class of coperfect modules lies properly between the class of locally artinian …

We provide some characterizations of rings R for which every (finitely generated) module
belonging to a class C of R-modules is a direct sum of cyclic submodules. We focus on the …

We introduce the concept of CMS modules. A right R-module M is called CMS if, every
closed M-cyclic submodule of M is a direct summand. An example of CMS module which is …

A module M is called a CS-module if every submodule of M is essential in a direct summand
of M. A ring R is called CS-semisimple if every right R-module is CS. For a ring R, we show …

Let R be a commutative ring with nonzero identity and M be an R-module. In this paper, we
introduce the concept of r-Artinian modules which is a new generalization of Artinian …

As a proper generalization of injective modules in term of supplements, we say that a
module M has the property (SE)(respectively, the property (SSE)) if, whenever M (N, M has a …

This paper continues the study of an R-module M through properties of the category a [M] of
submodules of M-generated modules. It is shown that a self-projective M is locally artinian if …

In this paper, we introduce and study the concept of CS-Rickart modules, that is a module
analogue of the concept of ACS rings. A ring R is called a right weakly semihereditary ring if …

Recall that an R-module M is pure-semisimple if every module in the category σ [M] is a
direct sum of finitely generated (and indecomposable) modules. A theorem from …

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) …