A left module $ M $ over an arbitrary ring is called an $\mathcal {RD} $-module (or an
$\mathcal {RS} $-module) if every submodule $ N $ of $ M $ with ${\rm Rad}(M)\subseteq N …

The purpose of the present paper is to prove some properties of the strongly irreducible
submodules in the arithmetical and Noetherian modules over a commutative ring. The …

Let R be a commutative ring with nonzero identity. Our objective is to investigate
representable modules and to examine in particular when submodules of such modules are …

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 …

In this note we compare some notions of primeness for modules existing in the literature. We
characterize the prime left R-modules such that the left annihilator of every element is a (two …

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 …

Let $ R $ be a commutative ring with identity and $ M $ be a unital $ R $-module. A proper
submodule $ N $ of $ M $ with $ N: _RM=\frak p $ is said to be prime or $\frak p $-prime …

We shall introduce the notion of uniformly classical primary submodule that generalizes the
concept of uniformly primary ideal as given by JA Cox and AJ Hetzel. We also advance the …

Let R be a commutative ring with identity and M be an R-module. As a new generalization of
primary ideals to modules, a proper submodule N of M is a primary-like submodule if …