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Abstract:

The notion of a Priestley relation between Priestley spaces is introduced, and it is shown that there is a duality between the category of bounded distributive lattices and 0-preserving join-homomorphisms and the category of Priestley spaces and Priestley relations. When restricted to the category of bounded distributive lattices and 0-1-preserving homomorphisms, this duality yields essentially Priestley duality, and when restricted to the subcategory of Boolean algebras and 0-preserving join-homomorphisms, it coincides with the Halmos-Wright duality. It is also established a duality between 0-1-sublattices of a bounded distributive lattice and certain preorder relations on its Priestley space, which are called lattice preorders. This duality is a natural generalization of the Boolean case, and is strongly related to one considered by M. E. Adams. Connections between both kinds of dualities are studied, obtaining dualities for closure operators and quantifiers. Some results on the existence of homomorphisms lying between meet and join homomorphisms are given in the Appendix. © 1991 Kluwer Academic Publishers.

Registro:

Documento: Artículo
Título:Remarks on Priestley duality for distributive lattices
Autor:Cignoli, R.; Lafalce, S.; Petrovich, A.
Filiación:Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Buenos Aires, 1428, Argentina
Palabras clave:AMS subject classification (1991): 06D05; Bounded distributive lattices; closure operators; filters; ideals; lattice homomorphisms; Priestley spaces; quantifiers; sublattices
Año:1991
Volumen:8
Número:3
Página de inicio:299
Página de fin:315
DOI: http://dx.doi.org/10.1007/BF00383451
Título revista:Order
Título revista abreviado:Order
ISSN:01678094
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01678094_v8_n3_p299_Cignoli

Referencias:

  • Ada, M.E., The Frattini sublattice of a distributive lattice (1973) Algebra Universalis, 3, pp. 216-228
  • Bacsich, P.D., Extension of Boolean homomorphisms with bounding semimorphisms (1972) J. reine angew. Math., 253, pp. 24-27
  • Balbes, R., Dwinger, P., (1979) Distributive Lattices, , University of Missouri Press, Columbia
  • Cignoli, R., A Hahn-Banach theorem for distributive lattices (1971) Rev. Un. Mat. Argentina, 25, pp. 335-342
  • R. Cignoli (1991) Quantifiers on distributive lattices, Discrete Math., to appear; Davis, C., Modal operators, equivalence relations, and projective algebras (1954) Amer. J. Math., 76, pp. 217-249
  • Graf, S., A selection theorem for Boolean correspondences (1977) J. reine angew. Math., 295, pp. 169-186
  • Gluschankof, D., Tilli, M., On some extensions theorems in functional analysis and the theory of Boolean algebras (1987) Rev. Un. Mat. Argentina, 33, pp. 44-54
  • Halmos, P.R., Algebraic logic, I. Monadic Boolean algebras (1955) Compositio Math., 12, pp. 217-249
  • Halmos, P.R., (1962) Algebraic Logic, , Chelsea Pub. Co., New York
  • Hansoul, G., A duality for Boolean algebras with operators (1983) Algebra Universalis, 17, pp. 34-49
  • Jónsson, B., Tarski, A., Boolean algebras with operators I (1951) American Journal of Mathematics, 73, pp. 891-938
  • Klimovsky, G., El teorema de Zorn y la existencia de filtros e ideales maximales en los reticulados distributivos (1958) Rev. Un. Mat. Argentina, 18, pp. 160-164
  • Kippelberg, S., Topological duality (1989) Handbook of Boolean Algebras, pp. 95-126. , J. D., Monk, R., Bonnet, North-Holland, Amsterdam-New York-Oxford-Tokyo
  • Monteiro, A., Généralisation d'un théorème de R. Sikorski sur les algèbres de Boole (1965) Bull. Sci. Math., 89 (2), pp. 65-74
  • Priestley, H.A., Representation of distributive lattices by means of ordered Stone spaces (1970) Bulletin of the London Mathematical Society, 2, pp. 186-190
  • Priestley, H.A., Ordered topological spaces and the representation of distributive lattices (1972) Proc. London Math. Soc., 2 (4), pp. 507-530
  • Priestley, H.A., Ordered sets and duality for distributive lattices (1984) Ann. Discrete Math., 23, pp. 39-60
  • Servi, M., Un'assiomatizzazione dei reticoli esistenziali (1979) Boll. Un. Mat. Ital. A, 16 (5), pp. 298-301
  • Vrancken-Mawet, L., The lattice of R-subalgebras of a bounded distributive lattice (1984) Comment. Math. Univ. Carolin., 25, pp. 1-17
  • Wright, F.B., Some remarks on Boolean duality (1957) Portugal. Math., 16, pp. 109-117

Citas:

---------- APA ----------
Cignoli, R., Lafalce, S. & Petrovich, A. (1991) . Remarks on Priestley duality for distributive lattices. Order, 8(3), 299-315.
http://dx.doi.org/10.1007/BF00383451
---------- CHICAGO ----------
Cignoli, R., Lafalce, S., Petrovich, A. "Remarks on Priestley duality for distributive lattices" . Order 8, no. 3 (1991) : 299-315.
http://dx.doi.org/10.1007/BF00383451
---------- MLA ----------
Cignoli, R., Lafalce, S., Petrovich, A. "Remarks on Priestley duality for distributive lattices" . Order, vol. 8, no. 3, 1991, pp. 299-315.
http://dx.doi.org/10.1007/BF00383451
---------- VANCOUVER ----------
Cignoli, R., Lafalce, S., Petrovich, A. Remarks on Priestley duality for distributive lattices. Order. 1991;8(3):299-315.
http://dx.doi.org/10.1007/BF00383451