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

TL;DR

This paper introduces the concept of quasi $z^ ext{o}$-submodules in modules over commutative rings, extending the idea of $z^ ext{o}$-ideals, and explores their properties in reduced multiplication modules.

Contribution

It defines quasi $z^ ext{o}$-submodules and investigates their properties specifically within reduced multiplication modules, extending existing ideal theory.

Findings

Defined quasi $z^ ext{o}$-submodules as an extension of $z^ ext{o}$-ideals.

Established properties of these submodules in reduced multiplication modules.

Connected the new notion to existing ideal theory concepts.

Abstract

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.