The aim of this paper is to study unitary regular modules on commutative rings with identity.
Regularity accompanied by cocyclic property results in some prime-related conclusions on …

All rings are associative with unity and modules are unital right modules. We use R to
denote such a ring and M to denote a right R-module. A module M is called CS or extending …

Let R be a commutative ring with identity. A proper submodule N of an R-module M will be
called prime [resp. n-almost prime], if for r∈ R and a∈ M with ra∈ N [resp. ra∈ N\(N: M) n …

In this paper we investigate the following two classes of left R-modules: N (P)={A| A has no
non-zero direct summand P ε P} and H (p)={A} if B⋚ A with B ε N (P), then B= 0}, where P is a …

Throughout, A represents an associative ring with identity and A-modules are unital. J, Z, Y
will denote respectively the Jacobson radical, the left singular ideal and the right singular …

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 $ and $ S $ be commutative rings and $ M $ an $(R, S) $-module. A proper $(R, S) $-
submodule $ P $ of $ M $ is called left weakly jointly prime if for each $(R, S) $-submodule …

A unital right R-module M is torsion free (abbreviation: tf) if its singular submodule ZM is ZM=
O. Essential submodules are denoted by"<<" and E (M) is the injective hull of M, eg M<< E …

A module M satisfies the restricted minimum condition if M/N is artinian for every essential
submodule N of M. A ring R is called a right RM-ring whenever $ R_ {R} $ satisfies the …