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.

primary spectrum‎, ‎primary Zariski topology‎, ‎primary submodule‎, ‎prime ideal