ON THE CLASSICAL PRIME SPECTRUM OF LATTICE MODULES

Year 2019, , 186 - 198, 08.01.2019

Pradip Girase Vandeo Borkar , Narayan Phadatare

https://doi.org/10.24330/ieja.504147

Cited By: 1

Abstract

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

$a ,b\in L$ 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.

 

Keywords

Classical prime element, classical prime spectrum, classical prime radical element, Zariski-like topology, spectral space

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