On the second spectrum of a module (II)

Let $R$ be a commutative ring and $M$ an $R$-module. Let $Spe{c}^s(M)$ be the the collection of all second submodules of $M$. In this article, we consider a new topology on $Spe{c}^s(M)$, called the second classical Zariski topology, and investigate the interplay between the module theoretic properties of $M$ and the topological properties of $Spe{c}^s(M)$. Moreover, we study $Spe{c}^s(M)$ from point of view of spectral space.