%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