Topologies on $Spec_g(M)$

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.