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This is a Quantitative Study study.

October 16, 2025Open Access

z^-submodules of a reduced multiplication module

Key Points

The study reveals the concept of z°-submodules, extending the notion of z°-ideals from rings to modules.
A proper ideal is classified as a z°-ideal if its intersection with minimal prime ideals is contained within itself.
The research investigates unique properties of z°-submodules specifically when associated with reduced multiplication modules.
Understanding z°-submodules can offer insights into their applications within the structure of R-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^-ideal if for each a 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^-submodules of M as an extension of z^-ideals of R. Moreover, we investigate some properties of this class of submodules when M is a reduced multiplication R-module.

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Cite This Study

F. Farshadifar (Thu,) studied this question.

synapsesocial.com/papers/68f147cc724575985c3fd244 https://doi.org/https://doi.org/10.48550/arxiv.2505.09961

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