TY - JOUR ID - 1766 TI - PRIMARY ZARISKI TOPOLOGY ON THE PRIMARY SPECTRUM OF A MODULE JO - Journal of Algebraic Systems JA - JAS LA - en SN - 2345-5128 AU - Bijari, H. AU - Khashyarmanesh, K. AU - Fazaeli Moghim, H. AD - Department of Pure Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159- 91775, Mashhad, Iran. AD - Department of Mathematics, University of Birjand, P.O. Box 97175-615, Birjand, Iran. Y1 - 2020 PY - 2020 VL - 8 IS - 1 SP - 53 EP - 68 KW - primary spectrum‎ KW - ‎primary Zariski topology‎ KW - ‎primary submodule‎ KW - ‎prime ideal DO - 10.22044/jas.2019.8320.1407 N2 - ‌‌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. UR - https://jas.shahroodut.ac.ir/article_1766.html L1 - https://jas.shahroodut.ac.ir/article_1766_bb94c6f535b2d77ed688e10b285d39ea.pdf ER -