| Title:
|
Modal operators on MV-algebras (English) |
| Author:
|
Harlenderová, Magdalena |
| Author:
|
Rachůnek, Jiří |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
131 |
| Issue:
|
1 |
| Year:
|
2006 |
| Pages:
|
39-48 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Modal operators on Heyting algebras were introduced by Macnab. In this paper we introduce analogously modal operators on MV-algebras and study their properties. Moreover, modal operators on certain derived structures are investigated. (English) |
| Keyword:
|
MV-algebra |
| Keyword:
|
modal operator |
| Keyword:
|
closure operator |
| Keyword:
|
residuated $\ell $-monoid |
| Keyword:
|
Heyting algebra |
| MSC:
|
06D25 |
| MSC:
|
06D35 |
| MSC:
|
06F05 |
| idZBL:
|
Zbl 1112.06014 |
| idMR:
|
MR2211002 |
| DOI:
|
10.21136/MB.2006.134083 |
| . |
| Date available:
|
2009-09-24T22:24:02Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134083 |
| . |
| Reference:
|
[1] Cignoli, R. L. O., D’Ottaviano, I. M. L., Mundici, D.: Algebraic Foundations of Many- valued Reasoning.Kluwer, Dordrecht, 2000. MR 1786097 |
| Reference:
|
[2] Dvurečenskij, A., Pulmannová, S.: New Trends in Quantum Structures.Kluwer Acad. Publ., Dordrecht, Ister Science, Bratislava, 2000. MR 1861369 |
| Reference:
|
[3] Macnab, D. S.: Modal operators on Heyting algebras.Algebra Univers. 12 (1981), 5–29. Zbl 0459.06005, MR 0608645, 10.1007/BF02483860 |
| Reference:
|
[4] Rachůnek, J.: Modal operators on ordered sets.Acta Univ. Palacki. Olomuc., Fac. Rer. Nat., Math. 24 (1985), 9–14. MR 0879015 |
| Reference:
|
[5] Rachůnek, J.: $DR\ell $-semigroups and MV-algebras.Czechoslovak Math. J. 48 (1998), 365–372. MR 1624268, 10.1023/A:1022801907138 |
| Reference:
|
[6] Rachůnek, J.: MV-algebras are categorically equivalent to a class of $DR\ell _{1(i)}$-semigroups.Math. Bohem. 123 (1998), 437–441. MR 1667115 |
| Reference:
|
[7] Rachůnek, J., Šalounová, D.: Local bounded commutative residuated $\ell $-monoids (submitted).. |
| Reference:
|
[8] Rachůnek, J., Švrček, F.: MV-algebras with additive closure operators.Acta Univ. Palacki. Olomuc., Fac. Rer. Mat., Math. 39 (2000), 183–189. MR 1826361 |
| . |
