Concerning the frame of minimal prime ideals of pointfree function rings | ||
| Categories and General Algebraic Structures with Applications | ||
| مقاله 3، دوره 1، شماره 1، اسفند 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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