PRIMARY ZARISKI TOPOLOGY ON THE PRIMARY SPECTRUM OF A MODULE
عنوان مقاله: PRIMARY ZARISKI TOPOLOGY ON THE PRIMARY SPECTRUM OF A MODULE
شناسه ملی مقاله: JR_JAS-8-1_006
منتشر شده در شماره 1 دوره 8 فصل در سال 1399
شناسه ملی مقاله: JR_JAS-8-1_006
منتشر شده در شماره 1 دوره 8 فصل در سال 1399
مشخصات نویسندگان مقاله:
H. Bijari - Department of Pure Mathematics, Ferdowsi University of Mashhad, P.O. Box ۱۱۵۹- ۹۱۷۷۵, Mashhad, Iran.
K. Khashyarmanesh - Department of Pure Mathematics, Ferdowsi University of Mashhad, P.O. Box ۱۱۵۹- ۹۱۷۷۵, Mashhad, Iran.
H. Fazaeli Moghim - Department of Mathematics, University of Birjand, P.O. Box ۹۷۱۷۵-۶۱۵, Birjand, Iran.
خلاصه مقاله:
H. Bijari - Department of Pure Mathematics, Ferdowsi University of Mashhad, P.O. Box ۱۱۵۹- ۹۱۷۷۵, Mashhad, Iran.
K. Khashyarmanesh - Department of Pure Mathematics, Ferdowsi University of Mashhad, P.O. Box ۱۱۵۹- ۹۱۷۷۵, Mashhad, Iran.
H. Fazaeli Moghim - Department of Mathematics, University of Birjand, P.O. Box ۹۷۱۷۵-۶۱۵, Birjand, Iran.
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.
کلمات کلیدی: primary spectrum, primary Zariski topology, primary submodule, prime ideal
صفحه اختصاصی مقاله و دریافت فایل کامل: https://civilica.com/doc/1041024/