Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
minimal prime; spectral topology; inverse topology; congruence
minimal prime; spectral topology; inverse topology; congruence
Summary:
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.
References:
[1] Belluce, L. P., Nola, A. Di, Sessa, S.: The prime spectrum of an MV-algebra. Math. Log. Q. 40 (1994), 331-346. DOI 10.1002/malq.19940400304 | MR 1283500 | Zbl 0815.06010
[2] Bhattacharjee, P., Drees, K. M., McGovern, W. W.: Extensions of commutative rings. Topology Appl. 158 (2011), 1802-1814. DOI 10.1016/j.topol.2011.06.015 | MR 2823692 | Zbl 1235.13006
[3] Chang, C. C.: Algebraic analysis of many valued logics. Trans. Am. Math. Soc. 88 (1958), 467-490. DOI 10.2307/1993227 | MR 0094302 | Zbl 0084.00704
[4] Cignoli, R. L. O., D'Ottaviano, I. M. L., Mundici, D.: Algebraic Foundations of Many-Valued Reasoning. Trends in Logic-Studia Logica Library 7. Kluwer Academic Publishers, Dordrecht (2000). DOI 10.1007/978-94-015-9480-6 | MR 1786097 | Zbl 0937.06009
[5] Eslami, E.: The prime spectrum on BL-algebras and MV-algebras. Siminar Algebra Tarbiat Moallem University (2009), 58-61 Persian.
[6] Forouzesh, F., Eslami, E., Saeid, A. Borumand: Spectral topology on MV-modules. New Math. Nat. Comput. 11 (2015), 13-33. DOI 10.1142/S1793005715500027 | MR 3325053 | Zbl 1376.06013
[7] Munkres, J. R.: Topology. Prentice Hall, Upper Saddle River (2000). MR 3728284 | Zbl 0951.54001
[8] Piciu, D.: Algebras of Fuzzy Logic. Editura Universitaria din Craiova, Craiova (2007), Romanian.
Search
Partner of
