PRIMARY ZARISKI TOPOLOGY ON THE PRIMARY SPECTRUM OF A MODULE | ||
| Journal of Algebraic Systems | ||
| مقاله 6، دوره 8، شماره 1، آذر 2020، صفحه 53-68 اصل مقاله (183.4 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22044/jas.2019.8320.1407 | ||
| نویسندگان | ||
| H. Bijari1؛ K. Khashyarmanesh* 1؛ H. Fazaeli Moghim2 | ||
| 1Department of Pure Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159- 91775, Mashhad, Iran. | ||
| 2Department of Mathematics, University of Birjand, P.O. Box 97175-615, Birjand, Iran. | ||
| چکیده | ||
| Let $R$ be a commutative ring with identity and let $M$ be an $R$-module. We define the primary spectrum of $M$, denoted by $\mathcal{PS}(M)$, to be the set of all primary submodules $Q$ of $M$ such that $(\operatorname{rad}Q:M)=\sqrt{(Q:M)}$. In this paper, we topologize $\mathcal{PS}(M)$ with a topology having the Zariski topology on the prime spectrum $\operatorname{Spec}(M)$ as a subspace topology. We investigate compactness and irreducibility of this topological space and provide some conditions under which $\mathcal{PS}(M)$ is a spectral space. | ||
| کلیدواژهها | ||
| primary spectrum؛ primary Zariski topology؛ primary submodule؛ prime ideal | ||
| مراجع | ||
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