@article {
author = {Bijari, H. and Khashyarmanesh, K. and Fazaeli Moghim, H.},
title = {PRIMARY ZARISKI TOPOLOGY ON THE PRIMARY SPECTRUM OF A MODULE},
journal = {Journal of Algebraic Systems},
volume = {8},
number = {1},
pages = {53-68},
year = {2020},
publisher = {Shahrood University of Technology},
issn = {2345-5128},
eissn = {2345-511X},
doi = {10.22044/jas.2019.8320.1407},
abstract = {Let $R$ be a commutative ring with identity and let $M$ be an $R$-module. We define the primary spectrum of $M$, denoted by $\mathcal{PS}(M)$, to be the set of all primary submodules $Q$ of $M$ such that $(\operatorname{rad}Q:M)=\sqrt{(Q:M)}$. In this paper, we topologize $\mathcal{PS}(M)$ with a topology having the Zariski topology on the prime spectrum $\operatorname{Spec}(M)$ as a subspace topology. We investigate compactness and irreducibility of this topological space and provide some conditions under which $\mathcal{PS}(M)$ is a spectral space.},
keywords = {primary spectrum,primary Zariski topology,primary submodule,prime ideal},
url = {https://jas.shahroodut.ac.ir/article_1766.html},
eprint = {https://jas.shahroodut.ac.ir/article_1766_bb94c6f535b2d77ed688e10b285d39ea.pdf}
}