| Title:
|
Notes on monadic $n$-valued Łukasiewicz algebras (English) |
| Author:
|
Figallo, A. V. |
| Author:
|
Pascual, I. |
| Author:
|
Ziliani, A. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
129 |
| Issue:
|
3 |
| Year:
|
2004 |
| Pages:
|
255-271 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A topological duality for monadic $n$-valued Łukasiewicz algebras introduced by M. Abad (Abad, M.: Estructuras cíclica y monádica de un álgebra de Łukasiewicz $n$-valente. Notas de Lógica Matemática 36. Instituto de Matemática. Universidad Nacional del Sur, 1988) is determined. When restricted to the category of $Q$-distributive lattices and $Q$-homomorphims, it coincides with the duality obtained by R. Cignoli in 1991. A new characterization of congruences by means of certain closed and involutive subsets of the associated space is also obtained. This allowed us to describe subdirectly irreducible algebras in this variety, arriving by a different method at the results established by Abad. (English) |
| Keyword:
|
$n$-valued Łukasiewicz algebras |
| Keyword:
|
Priestley spaces |
| Keyword:
|
congruences |
| Keyword:
|
subdirectly irreducible algebras |
| MSC:
|
03G20 |
| MSC:
|
06D30 |
| MSC:
|
06D50 |
| idZBL:
|
Zbl 1080.06011 |
| idMR:
|
MR2092712 |
| DOI:
|
10.21136/MB.2004.134149 |
| . |
| Date available:
|
2009-09-24T22:14:50Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134149 |
| . |
| Reference:
|
[1] Abad, M.: Estructuras cíclica y monádica de un álgebra de Łukasiewicz $n$-valente.Notas de Lógica Matemática 36. Inst. Mat. Univ. Nacional del Sur, Bahía Blanca, 1988. MR 0935965 |
| Reference:
|
[2] Balbes R.; Dwinger, P.: Distributive Lattices.Univ. of Missouri Press, Columbia, 1974. MR 0373985 |
| Reference:
|
[3] Bialynicki-Birula, A.; Rasiowa, H.: On the representation of quasi-Boolean algebras.Bull. Acad. Pol. Sci. C1. III 5 (1957), 259–261. MR 0087628 |
| Reference:
|
[4] Boicescu, V.; Filipoiu, A.; Georgescu, G.; Rudeanu, S.: Łukasiewicz-Moisil Algebras.North-Holland, Amsterdam, 1991. MR 1112790 |
| Reference:
|
[5] Burris, S.; Sankappanavar, H. P.: A Course in Universal Algebra.Graduate Texts in Mathematics, Vol. 78, Springer, Berlin, 1981. MR 0648287, 10.1007/978-1-4613-8130-3_3 |
| Reference:
|
[6] Cignoli, R.: Algebras de Moisil de orden $n$.Ph.D. Thesis. Univ. Nacional del Sur, Bahía Blanca, 1969. |
| Reference:
|
[7] Cignoli, R.: Moisil Algebras.Notas de Lógica Matemática 27. Instituto de Matemática Universidad Nacional del Sur, Bahía Blanca, 1970. Zbl 0212.31701, MR 0345884 |
| Reference:
|
[8] Cignoli, R.: Quantifiers on distributive lattices.Discrete Math. 96 (1991), 183–197. Zbl 0753.06012, MR 1139446, 10.1016/0012-365X(91)90312-P |
| Reference:
|
[9] Cignoli, R.; Lafalce, S.; Petrovich, A.: Remarks on Priestley duality for distributive lattices.Order 8 (1991), 299–315. MR 1154933, 10.1007/BF00383451 |
| Reference:
|
[10] Cornish, W. H.; Fowler, P. R.: Coproducts of de Morgan algebras.Bull. Austral. Math. Soc. 16 (1977), 1–13. MR 0434907, 10.1017/S0004972700022966 |
| Reference:
|
[11] Filipoiu, A.: Representation of Łukasiewicz algebras by means of ordered Stone spaces.Discrete Math. 30 (1980), 111–116. Zbl 0453.06011, MR 0566427, 10.1016/0012-365X(80)90112-0 |
| Reference:
|
[12] Filipoiu, A.: $\vartheta $-valued Łukasiewicz-Moisil algebras and logics.Ph.D. Thesis, Univ. of Bucharest, 1981. (Romanian) |
| Reference:
|
[13] Filipoiu, A.: Representation theorems for $\theta $-valued Łukasiewicz algebras.Discrete Math. 33 (1981), 21–27. Zbl 0455.06004, MR 0597224, 10.1016/0012-365X(81)90254-5 |
| Reference:
|
[14] Kalman, J. A.: Lattices with involution.Trans. Am. Math. Soc. 87 (1958), 485–491. Zbl 0228.06003, MR 0095135, 10.1090/S0002-9947-1958-0095135-X |
| Reference:
|
[15] Mac Lane, S.: Categories for the Working Mathematician.Springer, Berlin, 1988. |
| Reference:
|
[16] Moisil, Gr. C.: Le algebre di Łukasiewicz.An. Univ. Bucuresti, Ser. Acta Logica 6 (1963), 97–135. Zbl 0241.02007, MR 0173597 |
| Reference:
|
[17] Moisil, Gr. C.: Notes sur les logiques non-chrysippiennes.Ann. Sci. Univ. Jassy 27 (1941), 86–98. (French) Zbl 0025.29401, MR 0018621 |
| Reference:
|
[18] Monteiro, A.: Algebras de de Morgan.Curso dictado en la Univ. Nac. del Sur, Bahía Blanca, 1962. MR 1420008 |
| Reference:
|
[19] Priestley, H.: Representation of distributive lattices by means of ordered Stone spaces.Bull. Lond. Math. Soc. 2 (1970), 186–190. Zbl 0201.01802, MR 0265242, 10.1112/blms/2.2.186 |
| Reference:
|
[20] Priestley, H.: Ordered topological spaces and the representation of distributive lattices.Proc. Lond. Math. Soc. 4 (1972), 507–530. Zbl 0323.06011, MR 0300949, 10.1112/plms/s3-24.3.507 |
| Reference:
|
[21] Priestley, H.: Ordered sets and duality for distributive lattices.Ann. Discrete Math. 23 (1984), 39–60. Zbl 0557.06007, MR 0779844 |
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