In this note we consider a generalization of the notion of a purely extending modules,
defined using y–closed submodules. We show that a ring R is purely y–extending if and only …

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 …

Semiperfect modules were introduced by Mares [15] as a generalization of semiperfect
rings: A projective module P is called semiperfect when every quotient of P has a projective …

We study these rings with every minimal left ideal being a projective, direct summand and ap–
injective module, respectively. Some characterizations of these rings are given, and the …

Let R be a ring. A left R-module M (resp., right R-module N) is called weak injective (resp.,
weak flat) if (resp.,) for every super finitely presented left R-module F. By replacing finitely …

Throughout this paper all rings will be associative with identity and modules will be unital
right modules. A ring R is called right CS-ring (or extending ring) if every right ideal I in R is …

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 …

Let R be a ring with unity, and let M be an unitary R-module. In this work we present strongly
pure ideal (sub module) concept as a generalization of pure ideal (sub module). Also we …

Rings over which every nonzero right module has a maximal submodule are called right
Bass rings. For a ring A module-finite over its center C, the equivalence of the following …

In this paper, several characterizations of semi-compact modules are given. Among other
results, we study rings whose semi-compact modules are injective. We introduce the …