$z^\circ$-submodules of a reduced multiplication module

TL;DR

This paper introduces and studies $z^ullet$-submodules of modules over commutative rings, extending the concept of $z^ullet$-ideals, with a focus on reduced multiplication modules.

Contribution

It defines $z^ullet$-submodules of modules and explores their properties in the context of reduced multiplication modules, extending existing ideal theory.

Findings

Characterization of $z^ullet$-submodules in reduced multiplication modules

Properties and behaviors of these submodules within the module structure

Extension of $z^ullet$-ideal concepts from rings to modules

Abstract

Let R be a commutative ring with identity and M be an R-module. A proper ideal I of R is said to be a $z^\circ$-ideal if for each $a \in I$ the intersection of all minimal prime ideals containing a is contained in I. The purpose of this paper is to introduce the notion of $z^\circ$-submodules of M as an extension of $z^\circ$-ideals of R. Moreover, we investigate some properties of this class of submodules when M is a reduced multiplication R-module.