@article{article_504147, title={ON THE CLASSICAL PRIME SPECTRUM OF LATTICE MODULES}, journal={International Electronic Journal of Algebra}, volume={25}, pages={186–198}, year={2019}, DOI={10.24330/ieja.504147}, author={Girase, Pradip and Borkar, Vandeo and Phadatare, Narayan}, keywords={Classical prime element,classical prime spectrum,classical prime radical element,Zariski-like topology,spectral space}, abstract={<div> <span style="font-size: 12.6px;">Let $M$ be a lattice module over a $C$-lattice $L$. A proper element $P$ of $M$ is said to be classical prime if for </span> </div> <div> <span style="font-size: 12.6px;">$a ,b\in L$ and $X\in M, abX\leq P$ implies that $aX\leq P$ or $bX\leq P$. The set of all classical prime elements of $M$, $Spec^{cp}(M)$ is called as classical prime spectrum. In this article, we introduce and study a topology on $Spec^{cp}(M)$, called as Zariski-like topology of $M$. We investigate this topological space from the point of view of spectral spaces. We show that if $M$ has ascending chain condition on classical prime radical elements, then $Spec^{cp}(M)$ with the Zariski-like topology is a spectral space. </span> </div> <div> <span style="font-size: 12.6px;">  </span> </div>}, number={25}, publisher={Abdullah HARMANCI}