On minimal spectrum of multiplication lattice modules

Abstract

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

Keywords

• prime element
• mimimal prime element
• Zariski topology