The notion of δ-semiregular modules is introduced in terms of δ-small submodules. It is
shown that a ring R is a δ-semiregular ring if and only if RR is a δ-semiregular module, if and …

A module M is called a CS-module if every submodule of M is essential in a direct summand
of M. It is shown that a ring R is semilocal if and only if every semiprimitive right R-module is …

Let R be a ring with Jacobson radical J (R). Following CNI, a submodule N of a left R-
module RM is said to lie over a summand of M if there exists an idempotent e E End (RM) …

Let M be a left R-module and F a submodule of M for any ring R. We call MF-semiregular if
for every x∈ M, there exists a decomposition M= A⊕ B such that A is projective, A≤ Rx and …

For a ring R and a right R-module M, a submodule N of M is said to be δ-small in M if,
whenever N+ X= M with M/X singular, we have X= M. If there exists an epimorphism p: P→ M …

Strongly prime rings have been studied in the papers [2],[3],[6],[7],[8], Strongly prime
modules were introduced in [2], and then studied in [2],[8]. Strongly semiprime rings were …

An R-module M is called almost injective if M is a supplement submodule of every module
which contains M. The module M is called F-almost injective if every factor module of M is …

In this paper, we consider associative rings with unit and unitary modules over these rings.
Let R be a ring and M a right unitary R-module. We denote by J (R) and J (M) the Jacobson …

In this paper we shall generalize the notion of semiperfect modules in terms of preradicals,
and show that almost all properties of semiperfect modules are preserved under this …

Zhou defined\delta-semiperfect rings as a proper generalization of semiperfect rings. The
purpose of this paper is to discuss relative notions of supplemented modules and to show …