A Topological Aspect of the Graded Spectrum of a Graded Ring

Abstract

Let G be a group with identity e. Let R be a G-graded commutative ring. The set of all G-prime ideals of the graded Ring (R, G) which contains L denoted by V(L) for L \(\subseteq\)R. GX and GM are defined to be the set of all graded ideals and the set of all graded maximal ideas of (R, G) receptivity. In this paper, we define a topology on GX having the Zariski topology on the graded prime spectrum G-spec(R)=f{GX-V(L):L\(\subseteq\)R}, and investigate several topological properties of this topological space.