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We study the minimal prime elements of multiplication lattice module $M$ over a $C$-lattice $L$. Moreover, we topologize the spectrum $\pi \left(M\right)$ of minimal prime elements of $M$ and study several properties of it. The compactness of $\pi \left(M\right)$ is characterized in several ways. Also, we investigate the interplay between the topological properties of $\pi \left(M\right)$ and algebraic properties of $M$.