| Title:
|
Inverse topology in MV-algebras (English) |
| Author:
|
Forouzesh, Fereshteh |
| Author:
|
Sajadian, Farhad |
| Author:
|
Bedrood, Mahta |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
144 |
| Issue:
|
3 |
| Year:
|
2019 |
| Pages:
|
273-285 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
minimal prime |
| Keyword:
|
spectral topology |
| Keyword:
|
inverse topology |
| Keyword:
|
congruence |
| MSC:
|
06D35 |
| MSC:
|
06F30 |
| idZBL:
|
Zbl 07088851 |
| idMR:
|
MR3985857 |
| DOI:
|
10.21136/MB.2018.0117-17 |
| . |
| Date available:
|
2019-07-24T11:11:27Z |
| Last updated:
|
2020-07-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147774 |
| . |
| Reference:
|
[1] Belluce, L. P., Nola, A. Di, Sessa, S.: The prime spectrum of an MV-algebra.Math. Log. Q. 40 (1994), 331-346. Zbl 0815.06010, MR 1283500, 10.1002/malq.19940400304 |
| Reference:
|
[2] Bhattacharjee, P., Drees, K. M., McGovern, W. W.: Extensions of commutative rings.Topology Appl. 158 (2011), 1802-1814. Zbl 1235.13006, MR 2823692, 10.1016/j.topol.2011.06.015 |
| Reference:
|
[3] Chang, C. C.: Algebraic analysis of many valued logics.Trans. Am. Math. Soc. 88 (1958), 467-490. Zbl 0084.00704, MR 0094302, 10.2307/1993227 |
| Reference:
|
[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). Zbl 0937.06009, MR 1786097, 10.1007/978-94-015-9480-6 |
| Reference:
|
[5] Eslami, E.: The prime spectrum on BL-algebras and MV-algebras.Siminar Algebra Tarbiat Moallem University (2009), 58-61 Persian. |
| Reference:
|
[6] Forouzesh, F., Eslami, E., Saeid, A. Borumand: Spectral topology on MV-modules.New Math. Nat. Comput. 11 (2015), 13-33. Zbl 1376.06013, MR 3325053, 10.1142/S1793005715500027 |
| Reference:
|
[7] Munkres, J. R.: Topology.Prentice Hall, Upper Saddle River (2000). Zbl 0951.54001, MR 3728284 |
| Reference:
|
[8] Piciu, D.: Algebras of Fuzzy Logic.Editura Universitaria din Craiova, Craiova (2007), Romanian. |
| . |
