Dube, T. (2013). Concerning the frame of minimal prime ideals of pointfree function rings. Categories and General Algebraic Structures with Applications, 1(1), 11-26.

Themba Dube. "Concerning the frame of minimal prime ideals of pointfree function rings". Categories and General Algebraic Structures with Applications, 1, 1, 2013, 11-26.

Dube, T. (2013). 'Concerning the frame of minimal prime ideals of pointfree function rings', Categories and General Algebraic Structures with Applications, 1(1), pp. 11-26.

Dube, T. Concerning the frame of minimal prime ideals of pointfree function rings. Categories and General Algebraic Structures with Applications, 2013; 1(1): 11-26.

Concerning the frame of minimal prime ideals of pointfree function rings

^{}Department of Mathematical Sciences, University of South Africa, P.O. Box 392, 0003 Unisa, South Africa.

Abstract

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.

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