Artículo
Abstract:
It was shown in [3] (see also [5]) that there is a duality between the category of bounded distributive lattices endowed with a join-homomorphism and the category of Priestley spaces endowed with a Priestley relation. In this paper, bounded distributive lattices endowed with a join-homomorphism, are considered as algebras and we characterize the congruences of these algebras in terms of the mentioned duality and certain closed subsets of Priestley spaces. This enable us to characterize the simple and subdirectly irreducible algebras. In particular, Priestley relations enable us to characterize the congruence lattice of the Q-distributive lattices considered in [4]. Moreover, these results give us an effective method to characterize the simple and subdirectly irreducible monadic De Morgan algebras [7]. The duality considered in [4], was obtained in terms of the range of the quantifiers, and such a duality was enough to obtain the simple and subdirectly irreducible algebras, but not to characterize the congruences. © 1996 Kluwer Academic Publishers.
Registro:
| Documento: | Artículo |
| Título: | Distributive lattices with an operator |
| Autor: | Petrovich, A. |
| Filiación: | Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Ciudad Universitaria, 1428 Buenos Aires, Argentina |
| Palabras clave: | Bounded distributive lattices; Closure operators; Congruence relations; Join-homomorphisms; Lattice homomorphisms; Priestley relations; Priestley spaces; Quantifiers; Varieties |
| Año: | 1996 |
| Volumen: | 56 |
| Número: | 1-2 |
| Página de inicio: | 205 |
| Página de fin: | 224 |
| DOI: | http://dx.doi.org/10.1007/BF00370147 |
| Título revista: | Studia Logica |
| Título revista abreviado: | Stud. Logica |
| ISSN: | 00393215 |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00393215_v56_n1-2_p205_Petrovich |
Referencias:
- Blok, W.J., Dwinger, P.H., Equational classes of closure algebras (1975) Ind. Math., 37, pp. 189-198
- Cignoli, R., Distributive lattice congruences and Priestley spaces (1991) Actas Del Primer Congreso Dr. Antonio Monteiro, pp. 81-84. , Universidad Nacional del Sur, Bahía Bianca
- Cignoli, R., Lafalce, S., Petrovich, A., Remarks on Priestley duality for distributive lattices (1991) Order, 8, pp. 299-315
- Cignoli, R., Quantifiers on distributive lattices (1991) Discrete Math., 96, pp. 183-197
- Goldblatt, R., Varieties of Complex algebras (1989) Ann. Pure Appl. Logic., 44, pp. 173-242
- McKinsey, J.C.C., Tarski, A., The algebra of topology (1944) Ann. of Math., 45, pp. 141-191
- Petrovich, A., Monadic de Morgan Algebras, , to appear
- Priestley, H.A., Representation of distributive lattices by means of ordered Stone spaces (1970) Bull. London Math. Soc., 2, pp. 186-190
- Priestley, H.A., Ordered topological spaces and the representation of distributive lattices (1972) Proc. London Math. Soc., 3, pp. 507-530
- Priestley, H.A., Stone lattices: A topological approach (1974) Fund. Math., 84, pp. 127-143
- Priestley, H.A., Ordered sets and duality for distributive lattices (1984) Ann. Discrete Math., 23, pp. 39-60
- Rasiowa, H., Sikorski, R., (1963) The Mathematics of Metamathematics, , Warszawa
Citas:
---------- APA ----------
(1996) . Distributive lattices with an operator. Studia Logica, 56(1-2), 205-224.http://dx.doi.org/10.1007/BF00370147
---------- CHICAGO ----------
Petrovich, A. "Distributive lattices with an operator" . Studia Logica 56, no. 1-2 (1996) : 205-224.http://dx.doi.org/10.1007/BF00370147
---------- MLA ----------
Petrovich, A. "Distributive lattices with an operator" . Studia Logica, vol. 56, no. 1-2, 1996, pp. 205-224.http://dx.doi.org/10.1007/BF00370147
---------- VANCOUVER ----------
Petrovich, A. Distributive lattices with an operator. Stud. Logica. 1996;56(1-2):205-224.http://dx.doi.org/10.1007/BF00370147
