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arXiv · 2209.13534

The Zariski topology on the secondary like spectrum of a module

Saif Salam·Khaldoun Al-Zoubi
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Abstract

Let $R$ be a commutative ring with unity and $M$ be a left $R$-module. We define the secondary-like spectrum of $M$ to be the set of all secondary submodules $K$ of $M$ such that $Ann_R(soc(K))=\sqrt{Ann_R(K)}$, and we denote it by $Spec^L(M)$. In this paper, we introduce a topology on $Spec^L(M)$ having the Zariski topology on the second spectrum $Spec^s(M)$ as a subspace topology, and study several topological structures of this topology.

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Saif Salam, Khaldoun Al-Zoubi. 2022-09-10. The Zariski topology on the secondary like spectrum of a module. https://doi.org/10.1515/math-2024-0005

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