@article {
author = {Dube, Themba},
title = {Concerning the frame of minimal prime ideals of pointfree function rings},
journal = {Categories and General Algebraic Structures with Applications},
volume = {1},
number = {1},
pages = {11-26},
year = {2013},
publisher = {Shahid Beheshti University},
issn = {2345-5853},
eissn = {2345-5861},
doi = {},
abstract = {Let $L$ be a completely regular frame and $mathcal{R}L$ be the ring of continuous real-valued functions on $L$. We study the frame $mathfrak{O}(Min(mathcal{R}L))$ of minimal prime ideals of $mathcal{R}L$ in relation to $beta L$. For $Iinbeta L$, denote by $textit{textbf{O}}^I$ the ideal ${alphainmathcal{R}Lmidcozalphain I}$ of $mathcal{R}L$. We show that sending $I$ to the set of minimal prime ideals not containing $textit{textbf{O}}^I$ produces a $*$-dense one-one frame homomorphism $beta Ltomathfrak{O}(Min(mathcal{R}L))$ which is an isomorphism if and only if $L$ is basically disconnected.},
keywords = {frame,ring of real-valued continuous functions on a
frame,minimal prime ideal,basically disconnected},
url = {https://cgasa.sbu.ac.ir/article_4263.html},
eprint = {https://cgasa.sbu.ac.ir/article_4263_6f79ee547811c22128d166583042a1da.pdf}
}