%0 Journal Article
%T Concerning the frame of minimal prime ideals of pointfree function rings
%J Categories and General Algebraic Structures with Applications
%I Shahid Beheshti University
%Z 2345-5853
%A Dube, Themba
%D 2013
%\ 12/01/2013
%V 1
%N 1
%P 11-26
%! Concerning the frame of minimal prime ideals of pointfree function rings
%K frame
%K ring of real-valued continuous functions on a
frame
%K minimal prime ideal
%K basically disconnected
%R
%X 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.
%U https://cgasa.sbu.ac.ir/article_4263_6f79ee547811c22128d166583042a1da.pdf