Abstract We present $* $-primary submodules, a generalization of the concept of primary
submodules of an $ R $-module. We show that every primary submodule of a Noetherian …

A (von Neumann) regular ring R is called to satisfy the property (DF) if every direct sum of
two directly finite projective R-modules is directly finite. We give new constructions of unit …

Results gotten for a module M over a commutative ring have been broadened to module
over a ring which is not necessarily commutative. It has been indicated that an R-module M …

We introduced and studied 𝐺𝐹-regular modules as a generalization of 𝜋-regular rings to
modules as well as regular modules (in the sense of Fieldhouse). An 𝑅-module 𝑀 is called …

In this study, we introduce the concepts of $ S $-prime submodules and\$ S $%-torsion-free
modules, which are generalizations of prime submodules and torsion-free modules …

In this paper all rings are commutative with nonzero identity. Let $ M $ be an $ R $-module.
A proper submodule $ N $ of $ M $ is called a {\it classical primary submodule}, if for each …

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 …

Let $ R $ be a commutative ring with identity and let $ M $ be an $ R $-module. A proper
submodule $ N $ of $ M $ is said to be an $ r $-submodule if $ am\in N $ with $(0: _Ma)= 0 …

Let be an endomorphism of an arbitrary ring R with identity and let M be a right R-module.
We introduce the notion of-symmetric modules as a generalization of-reduced modules. A …

In this paper, all rings are commutative with nonzero identity. Let $ M $ be an $ R $-module.
A proper submodule $ N $ of $ M $ is called a classical prime submodule, if for each $ m\in …