concerning the frame of minimal prime ideals of pointfree function rings
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abstract
let $l$ be a completely regular frame and $mathcal{r}l$ be the ringof 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 $iinbeta l$, denoteby $textit{textbf{o}}^i$ the ideal${alphainmathcal{r}lmidcozalphain i}$ of $mathcal{r}l$. weshow that sending $i$ to the set of minimal prime ideals notcontaining $textit{textbf{o}}^i$ produces a $*$-dense one-oneframe homomorphism $beta ltomathfrak{o}(min(mathcal{r}l))$which is an isomorphism if and only if $l$ is basicallydisconnected.
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Journal title:
categories and general algebraic structures with applicationsPublisher: shahid beheshti university
ISSN 2345-5853
volume 1
issue 1 2013
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