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

Rok, strany: 2019, 7 - 16

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 $r_gs_h\in P$, 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.

ISO 690:

Al-Zoubi, K., Jaradat, M. 2019. The Zariski topology on the graded primary spectrum over graded commutative rings. In Tatra Mountains Mathematical Publications, vol. 74, no.2, pp. 7-16. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2019-0015

APA:

Al-Zoubi, K., Jaradat, M. (2019). The Zariski topology on the graded primary spectrum over graded commutative rings. Tatra Mountains Mathematical Publications, 74(2), 7-16. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2019-0015

Vydavateľ: Mathematical Institute, Slovak Academy of Sciences, Bratislava

Licensed under the Creative Commons Attribution-NC-ND4.0 International Public License.