Zariski topology on the spectrum of graded classical prime submodules

Ahmad Yousefian Darani, Shahram Motmaen


Let $R$ be a $G$-graded commutative ring with identity and let $M$ be a graded $R$-module. A proper graded submodule $N$ of $M$ is called graded classical prime if for every $a, b\in h(R)$, $m\in h(M)$, whenever $abm\in N$, then either $am\in N$ or $bm\in N$. The spectrum of graded classical prime submodules of $M$ is denoted by $Cl.Spec_g(M)$. We topologize $Cl.Spec_g(M)$ with the quasi-Zariski topology, which is analogous to that for $Spec_g(R)$.


Graded prime ideal; Zariski topology; Quasi-Zariski topology

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Boletim da Sociedade Paranaense de Matemática  vol: 39  issue: 3  first page: 17  year: 2021  
doi: 10.5269/bspm.39909

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