Themba Dube - Department of Mathematical Sciences, University of South Africa, P.O. Box ۳۹۲, ۰۰۰۳ Unisa, South Africa.

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.

frame, ring of real-valued continuous functions on a frame, minimal prime ideal, basically disconnected