Quasi z∘z^\circ-submodules of a reduced multiplication

Let R be a commutative ring with identity and M be an R-module. The purpose of this paper is to defined the notion of quasi $z^\circ$-submodules of M as an extension of $z^\circ$-ideals of R and obtained some related results when M is a reduced multiplication R-module

The dual of z-submodules of modules and some of extensions

Let R be a commutative ring with identity and M be an R-module. The purpose of this paper is to introduced the dual notion of z-submodules of M and some of extensions. Moreover, we investigate some properties of these classes of modules when M is a coreduced comultiplication R-module

On endomorphisms of multiplication and comultiplication modules

summary:Let $R$ be a ring with an identity (not necessarily commutative) and let $M$ be a left $R$-module. This paper deals with multiplication and comultiplication left $R$-modules $M$ having right $\operatorname{End}_R(M)$-module structures

S-second submodules of a module

Let R be a commutative ring with identity and let M be an R-module. The main purpose of this paper is to introduce and study the notion of S-second submodules of an R-module M as a generalization of second submodules of M

Generalized 2-absorbing and strongly generalized 2-absorbing second submodules

In this paper, we will introduce the concepts of generalized 2-absorbing and strongly generalized 2-absorbing second submodules of modules over a commutative ring and obtain some related results