The Zariski topology on the secondary like spectrum of a module
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866929309826940928 |
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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 |