The Relationships Between Graded Ideals and Subspaces

This paper deals with the relationships between open subspaces of Zari.ski topology on graded prime ideals and graded ideals of a graded ring. After obtaining some algebraic and topological characterizations for a graded ring and Zariski topology on graded prime ideals, we finally prove that X-G = (i-1)boolean OR(n) X-G(Ii),, where I-i is irreducible and /i is a graded ideal of a graded ring R, if and only if R = (i=1)Sigma(n) I-i and N-G(Ii) (0) is a graded prime ideal of R.