Within the paper, we study the class of modules in which the direct sum of two disjoint
summands that is a pure submodule is also a summand. This class of modules is …

Let ℱ 𝒫∞ R be the class of all left R-modules M which has a projective resolution by finitely
generated projectives. An exact sequence 0→ A→ B→ C→ 0 of right R-modules is called …

Let R be a ring with Jacobson radical J. Bass [1] called R semi-perfect if the factor ring R/J is
semi-simple Artinian and every idempotent of R/J can be lifted to an idempotent of R. He …

In the last decade, two new approaches have been introduced for the analysis of the
projectivity of modules. In this paper, the projectivity of modules has been studied with a new …

A module M over a ring R is called n-injective (also called quasi-continuous) if for every pair
of R-submodules N,, N, of M with N, n N,=(0) each projection n,: N, SN,-N, i= 1, 2, can be …

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 …

Carl Faith (2003) introduced and investigated an interesting class of rings over which every
cyclic right module has Σ-injective injective hull (abbr., right CSI-rings). Inspired by this we …

Let R be an associative ring with identity and M be a left R-module. In this paper, we define
modules that have the property (δ-CE)((δ-CEE)), these are modules that have a δ …

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 …

Fieldhouse observed that any finitely presented left R-module P is projective with respect to
pure exact sequences, ie can always be completed to a commutative diagram when the …