The Zariski topology on the graded primary spectrum over graded commutative rings

Abstract

Let $G$ be a group with identity $e$ and let $R$ be a $G$-graded ring. A
proper graded ideal $P$ of $R$ is called \textit{a graded primary ideal}
if whenever $r_{g}s_{h}\in P$, we have $r_{g}\in P$ or $s_{h}\in Gr(P)$,
where $r_{g},s_{g}\in h(R).$ The \textit{graded primary spectrum } $%
p.Spec_{g}(R)$ is defined to be the set of all graded primary ideals of $R$.
In this paper, we define a topology on $p.Spec_{g}(R),$ called Zariski
topology, which is analogous to that for $Spec_{g}(R),$ and
investigate several properties of the topology.