Concerning the frame of minimal prime ideals of pointfree function rings

	Concerning the frame of minimal prime ideals of pointfree function rings
Categories and General Algebraic Structures with Applications
مقاله 3، دوره 1، شماره 1، 2013، صفحه 11-26 اصل مقاله (639.31 K)
نوع مقاله: Research Paper
نویسنده
Themba Dube
Department of Mathematical Sciences, University of South Africa, P.O. Box 392, 0003 Unisa, South Africa.
چکیده
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.
کلیدواژه‌ها
frame؛ ring of real-valued continuous functions on a frame؛ minimal prime ideal؛ basically disconnected
مراجع

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