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arXiv · 2109.10113

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

Saif Salam·Khaldoun Al-Zoubi
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Abstract

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 paper, we define a topology on $\mathcal{PS}_G(M)$ having the Zariski topology on the graded prime spectrum $Spec_G(M)$ as a subspace topology, and investigate several topological properties of this topological space.

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Saif Salam, Khaldoun Al-Zoubi. 2021-09-21. The Zariski topology on the graded primary spectrum of a graded module over a graded commutative ring. https://doi.org/10.4995/agt.2022.16332

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