@article {
author = {Borkar, V. and Girase, P. and Phadatare, N.},
title = {Classical Zariski Topology on Prime Spectrum of Lattice Modules},
journal = {Journal of Algebra and Related Topics},
volume = {6},
number = {2},
pages = {1-14},
year = {2018},
publisher = {University of Guilan},
issn = {2345-3931},
eissn = {2382-9877},
doi = {10.22124/jart.2018.11106.1112},
abstract = {Let $M$ be a lattice module over a $C$-lattice $L$. Let $Spec^{p}(M)$ be the collection of all prime elements of $M$. In this article, we consider a topology on $Spec^{p}(M)$, called the classical Zariski topology and investigate the topological properties of $Spec^{p}(M)$ and the algebraic properties of $M$. We investigate this topological space from the point of view of spectral spaces. By Hochster's characterization of a spectral space, we show that for each lattice module $M$ with finite spectrum, $Spec^{p}(M)$ is a spectral space. Also we introduce finer patch topology on $Spec^{p}(M)$ and we show that $Spec^{p}(M)$ with finer patch topology is a compact space and every irreducible closed subset of $Spec^{p}(M)$ (with classical Zariski topology) has a generic point and $Spec^{p}(M)$ is a spectral space, for a lattice module $M$ which has ascending chain condition on prime radical elements.},
keywords = {prime element,prime spectrum,classical Zariski topology,finer patch topology},
url = {https://jart.guilan.ac.ir/article_3326.html},
eprint = {https://jart.guilan.ac.ir/article_3326_5f999e1eaeb83e79b53a441a2df5103f.pdf}
}