The Zariski Topology on the Graded Primary Spectrum Over Graded Commutative Rings

Let G be a group with identity e and let R be a G-graded ring. A proper graded ideal P of R is called a graded primary ideal if whenever r_gs_h∈P, we have r_g∈ P or s_h∈ Gr(P), where r_g,s_g∈ h(R). The graded primary spectrum p.Spec_g(R) is defined to be the set of all graded primary ideals of R.In this paper, we define a topology on p.Spec_g(R), called Zariski topology, which is analogous to that for Spec_g(R), and investigate several properties of the topology.