Shahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-58531120131201Concerning the frame of minimal prime ideals of pointfree function rings11264263ENThemba DubeDepartment of Mathematical Sciences, University of South Africa, P.O.
Box 392, 0003 Unisa, South Africa.Journal Article20140118Let $L$ 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.https://cgasa.sbu.ac.ir/article_4263_6f79ee547811c22128d166583042a1da.pdf