In this paper, we investigate some properties of SIP, SSP and CS-Rickart modules. We give
equivalent conditions for SIP and SSP modules; establish connections between the class of …

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 …

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 …

We investigate some properties of Rickart modules defined by Rizvi and Roman. Let R be
an arbitrary ring with identity and M be a right R-module with S= EndR (M). A module M is …

ABSTRACT A right R-module M is called simple-direct-injective if, whenever, A and B are
simple submodules of M with A≅ B, and B⊆⊕ M, then A⊆⊕ M. Dually, M is called simple …

Abstract A module M is CS if every submodule of M is essential in a direct summand of M. In
this note we use the CS condition to provide conditions for semiperfect rings to be self …

All rings will be commutative with identity. A module M is called Π-semiartinian if the direct
product MI is a semiartinian module for every nonempty set I. A ring R is said to be Π …

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 …

Let $ R $ be an arbitrary ring with identity and $ M $ a right $ R $-module with $ S= $ End $
_R (M) $. In this paper we introduce $\pi $-Rickart modules as a generalization of Rickart …