An Additional Properties of the Graded Prime Spectrum of (R, G)

Abstract

Let G be a group and R be a G −graded commutative ring, i.e., \U0001d445\U0001d454 and \U0001d445\U0001d454\U0001d445ℎ ⊆ \U0001d445\U0001d454ℎ for all \U0001d454, ℎ ∈ \U0001d43a. For \U0001d43f ⊆ \U0001d445, let \U0001d449(\U0001d43f) denote the set of all \U0001d43a-prime ideals of (\U0001d445, \U0001d43a) containing \U0001d43f. Also, let \U0001d43a\U0001d44b denote the set of all graded prime ideals of (\U0001d445, \U0001d43a) and \U0001d43aℳ denote the set of all graded maximal ideals of (\U0001d445, \U0001d43a). Then Ƒ {\U0001d43a\U0001d44b − \U0001d449(\U0001d43f): \U0001d43f ⊆ \U0001d445} is a topological space G − spec(R) on \U0001d43a\U0001d44b. In this paper, we give an additional topological properties of G − spec(R).