Zariski topology on the spectrum of graded classical prime submodules

Ahmad Yousefian Darani

Iran, Islamic Republic of

University of Mohaghegh Ardabil

Shahram Motmaen

Iran, Islamic Republic of

Ardabil Branch Islamic Azad University

Submitted: 2013-07-15

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Accepted: 2013-07-21

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Published: 2013-07-21

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

Graded prime ideal, Zariski topology, Quasi-Zariski topology

Supporting agencies:

This research was not funded

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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