Geodesic
Inverse topology in MV-algebras
Mathematica Bohemica, Tome 144 (2019) no. 3, pp. 273-285
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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. \endgraf 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.
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. \endgraf 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.
DOI : 10.21136/MB.2018.0117-17
Classification : 06D35, 06F30
Keywords: minimal prime; spectral topology; inverse topology; congruence 
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Forouzesh, Fereshteh; Sajadian, Farhad; Bedrood, Mahta. Inverse topology in MV-algebras. Mathematica Bohemica, Tome 144 (2019) no. 3, pp. 273-285. doi: 10.21136/MB.2018.0117-17

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