Abstract
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.
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