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

TL;DR

This paper introduces the dual concept of z-submodules in modules over a commutative ring and explores their properties, especially when the module is coreduced and has a comultiplication structure.

Contribution

It defines the dual of z-submodules and studies their properties in the context of coreduced comultiplication modules, extending existing module theory.

Findings

Characterization of dual z-submodules

Properties of these modules in specific classes

Extensions related to dual z-submodules

Abstract

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.