Received October 15, 2017. Published online September 25, 2018.
Abstract: We introduce the inverse topology on the set of all minimal prime ideals of an MV-algebra $A$ and show that the set of all minimal prime ideals of $A$, namely ${\rm Min}(A)$, with the inverse topology is a compact space, Hausdorff, $T_0$-space and $T_1$-space. Furthermore, we prove that the spectral topology on ${\rm Min}(A)$ is a zero-dimensional Hausdorff topology and show that the spectral topology on ${\rm Min}(A)$ is finer than the inverse topology on ${\rm Min}(A)$. Finally, by open sets of the inverse topology, we define and study a congruence relation of an MV-algebra.
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Affiliations: Fereshteh Forouzesh, Farhad Sajadian, Mahta Bedrood, Faculty of Mathematics and Computing, Higher Education Complex of Bam, Khalij Fars street, 76613-14477 Bam, Kerman, Iran, e-mail: frouzesh@bam.ac.ir, fsajadian@bam.ac.ir, bedrood.m@gmail.com
