The Zariski topology on the secondary like spectrum of a module

Fuente: arXiv
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Main Authors: Salam, Saif, Al-Zoubi, Khaldoun
Format: Preprint
Published: 2022
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author Salam, Saif
Al-Zoubi, Khaldoun
author_facet Salam, Saif
Al-Zoubi, Khaldoun
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2209_13534
institution arXiv
publishDate 2022
record_format arxiv
spellingShingle The Zariski topology on the secondary like spectrum of a module
Salam, Saif
Al-Zoubi, Khaldoun
General Mathematics
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.
title The Zariski topology on the secondary like spectrum of a module
topic General Mathematics
url https://arxiv.org/abs/2209.13534