This article is cited in 2 papers

Topologies on $Spec_g(M)$

Ahmad Yousefian Darani

Department of Mathematics, University of Mohaghegh Ardabili, Ardabil, Iran

Abstract: Let $R$ be a $G$-graded commutative ring with identity and let $M$ be a graded $R$-module. We endow $Spec_g(M)$, the collection of all graded prime submodules of $M$, analogous to that for $Spec(R)$, the spectrum of prime ideals of $R$, by two topologies: quasi-Zariski topology and Zariski topology. Then we study some properties of these topological spaces.

Keywords and phrases: graded prime ideal, Zariski topology, quasi-Zariski topology.

MSC: 13A02, 16W50

Received: 13.01.2011

Language: English

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