Zariski topology on the spectrum of graded classical prime submodules

Ahmad Yousefian Darani; Shahram Motmaen

doi:10.4995/agt.2013.1586

Authors

Ahmad Yousefian Darani University of Mohaghegh Ardabil
Shahram Motmaen Ardabil Branch Islamic Azad University

DOI:

https://doi.org/10.4995/agt.2013.1586

Keywords:

Graded prime ideal, Zariski topology, Quasi-Zariski topology

Abstract

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 $Spec_g(R)$.

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