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arXiv · 2505.09961

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

F. Farshadifar
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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.

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F. Farshadifar. 2025-05-15. $z^\circ$-submodules of a reduced multiplication module. https://arxiv.org/abs/2505.09961

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