On the spectrum of a module over a commutative ring

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 h(R), m h(M ), whenever abm N , then either am N or bm N . The spectrum of graded classical prime submodules of M is denoted by Cl.Specg(M ). We topologize Cl.Specg(M ) with the quasi-Zariski topology, which is analogous to that for Specg(R).