ZARISKI TOPOLOGIES ON GRADED IDEALS
Abstract
In this article, we show how there are strong relations between al-
gebraic properties of a graded commutative ring R and topological properties of open subsets of Zariski topology on the graded prime spectrum of R. We examine some algebraic conditions for open subsets of Zariski topology to become quasi-compact, dense and irreducible. We also present a characterization for the radical of a graded ideal in R by using topological properties.
gebraic properties of a graded commutative ring R and topological properties of open subsets of Zariski topology on the graded prime spectrum of R. We examine some algebraic conditions for open subsets of Zariski topology to become quasi-compact, dense and irreducible. We also present a characterization for the radical of a graded ideal in R by using topological properties.