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Akademický článek

Zariski topology on the secondary-like spectrum of a module

Publikováno v: Open Mathematics, Vol 22, Iss 1, Pp 1350024-275 (2024)

Let ℜ\Re be a commutative ring with unity and ℑ\Im be a left ℜ\Re -module. We define the secondary-like spectrum of ℑ\Im to be the set of all secondary submodules KK of ℑ\Im such that the annihilator of the socle of KK is the radical of the

Externí odkaz: https://doaj.org/article/cccea454014649689dc0250dd54d2727

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The Zariski topology on the secondary like spectrum of a module

Autor: Salam, Saif, Al-Zoubi, Khaldoun

Publikováno v: Open Mathematics 2024; 22: 20240005

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 th

Externí odkaz: http://arxiv.org/abs/2209.13534

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Graded modules with Noetherian graded second spectrum

Autor: Salam, Saif, Al-Zoubi, Khaldoun

Publikováno v: AIMS Mathematics,2023

Let $R$ be a $G$ graded commutative ring and $M$ be a $G$-graded $R$-module. The set of all graded second submodules of $M$ is denoted by $Spec_G^s(M)$ and it is called the graded second spectrum of $M$. In this paper, we discuss graded rings with No

Externí odkaz: http://arxiv.org/abs/2207.10575

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The Zariski topology on the graded primary spectrum of a graded module over a graded commutative ring

Autor: Salam, Saif, Al-Zoubi, Khaldoun

Publikováno v: Applied General Topology,2022

Let $R$ be a $G$-graded ring and M be a $G$-graded $R$-module. We define the graded primary spectrum of $M$, denoted by $\mathcal{PS}_G(M)$, to be the set of all graded primary submodules $Q$ of M such that $(Gr_M(Q):_R M)=Gr((Q:_R M))$. In this pape

Externí odkaz: http://arxiv.org/abs/2109.10113

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