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

In: Tatra Mountains Mathematical Publications, vol. 74, no. 2

Details:

Year, pages: 2019, 7 - 16
Language: eng
Keywords:
Article type: mathematics
Document type: Scientific article *.pdf
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 $rgsh\in P$, we have $rg\in P$ or $sh\in Gr(P)$, where $rg,sg\in h(R).$ The \textit{graded primary spectrum} $p.Specg(R)$ is defined to be the set of all graded primary ideals of $R$. In this paper, we define a topology on $p.Specg(R),$ called Zariski topology, which is analogous to that for $Specg(R),$ and investigate several properties of the topology.