THE ZARISKI TOPOLOGY ON THE GRADED CLASSICAL PRIME SPECTRUM OF A GRADED MODULE OVER A GRADED COMMUTATIVE RING

Let G be a group with identity e. Let R be a G-graded commutative ring and M a graded R-module. A proper graded submodule N of M is called a graded classical prime if whenever r, s is an element of h(R) and m is an element of h(M) with rsm is an element of N, then either rm is an element of N or sm is an element of N. The graded classical prime spectrum Cl.Spec(g) (M) is defined to be the set of all graded classical prime submodules of M. In this paper, we introduce and study a topology on Cl.Spec(g) (M), which generalizes the Zariski topology of graded ring R to graded module M, called Zariski topology of M, and investigate several properties of the topology.