Navegar

Colección

Datos Estadísticas

Artículo

Estamos trabajando para incorporar este artículo al repositorio
Consulte el artículo en la página del editor
Consulte la política de Acceso Abierto del editor

Abstract:

The laws defining many important varieties of lattice-ordered algebras, such as linear Heyting algebras, MV-algebras and l-groups, can be cast in a form which allows dual representations to be derived in a very direct, and semi-automatic, way. This is achieved by developing a new duality theory for implicative lattices, which encompass all the varieries above. The approach focuses on distinguished subsets of the prime lattice filters of an implicative lattice, ordered as usual by inclusion. A decomposition theorem is proved, and the extent to which the order on the prime lattice filters determines the implicative structure is thereby revealed.

Registro:

Documento: Artículo
Título:On Priestley Spaces of Lattice-Ordered Algebraic Structures
Autor:Martínez, N.G.; Priestley, H.A.
Filiación:Depto. de Matematica, Fac. Cs. Exactas y Naturales, Ciudad Universitaria, (1428) Buenos Aires, Argentina
Mathematical Institute, 24/29 St Giles, Oxford OX1 3LB, United Kingdom
Palabras clave:Duality; Implicative lattice; Lattice-ordered group; Priestley space
Año:1998
Volumen:15
Número:4
Página de inicio:297
Página de fin:323
DOI: http://dx.doi.org/10.1023/A:1006224930256
Título revista:Order
Título revista abreviado:Order
ISSN:01678094
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01678094_v15_n4_p297_Martinez

Referencias:

  • Balbes, R., Dwinger, P., (1974) Distributive Lattices, , University of Missouri Press, Columbia, Missouri
  • Bigard, A., Keimel, K., Wolfenstein, S., Groupes et Anneaux Réticulés (1977) Lecture Notes in Math, 608. , Springer-Verlag, Berlin
  • Blyth, T.S., Varlet, J.C., (1994) Ockham Algebras, , Oxford University Press, Oxford
  • Cignoli, R., Elliot, T., Mundici, D., Reconstructing C*-algebras from their Murray von Neumann orders (1993) Adv. in Math., 101, pp. 166-179
  • Cignoli, R., Torrens, A., (1992) Ordered Spectra and Boolean Products of MV-algebras, , Preprint, Centre de Recerca Matematica, Institut D'Estudis Catalans, no 172, Barcelona
  • Chang, C.C., Algebraic analysis of many valued logics (1958) Trans. Amer. Math. Soc., 88, pp. 467-490
  • Cornish, W.H., Fowler, P.R., Coproducts of de Morgan Algebras (1977) Bull. Austral. Math. Soc., 16, pp. 1-13
  • Davey, B.A., Priestley, H.A., (1990) Introduction to Lattices and Order, , Cambridge University Press, Cambridge
  • Davey, B.A., Werner, H., Dualities and equivalences for varieties of algebras (1983) Contributions to Lattice Theory, , A. P. Huhn and E. T. Schmidt (eds.), (Szeged, 1980)
  • Colloq. Math. Soc. János Bolyai, 33, pp. 101-275. , North-Holland, Amsterdam
  • Font, J., Rodriguez, A.J., Torrens, A., Wajsberg algebras (1984) Stochastica, 8 (1), pp. 5-31
  • Glass, A.M., Holland, W.Ch., (1989) Lattice-Ordered Groups, , Kluwer Academic Publishers, Dordrecht
  • Horn, A., Logic with truth values in a linearly ordered Heyting algebra (1969) J. Symbolic Logic, 34, pp. 395-408
  • Martínez, N.G., The Priestley duality for Wajsberg algebras (1990) Studia Logica, 49, pp. 31-46
  • Martínez, N.G., A topological duality for some lattice-ordered algebraic structures including l-groups (1994) Algebra Universalis, 31, pp. 516-541
  • Martínez, N.G., A simplified duality for implicative lattices and l-groups (1996) Studia Logica, 56, pp. 185-204
  • Martínez, N.G., A reduced spectrum for MV-algebras Contemporary Mathematics
  • Monteiro, A., Sur les algebres de Heyting symétriques (1980) Portugal. Math., 39
  • Mundici, D., Interpretation of AF-C*-Algebras in Łukasiewicz sentential calculus (1986) J. Funct. Anal., 65, pp. 15-63
  • Priestley, H.A., Representation of distributive lattices by means of ordered Stone spaces (1972) Bull. London Math. Soc., 2, pp. 186-190
  • Priestley, H.A., Ordered topological spaces and the representation of distributive lattices (1975) Proc. London Math. Soc. 3, 24, pp. 507-530
  • Rasiowa, H., (1974) An Algebraic Approach to Non-Classical Logics, 78. , Studies in Logic, North-Holland, Amsterdam
  • Urquhart, A., Distributive lattices with a dual homomorphic operation (1979) Studia Logica, 38, pp. 201-209

Citas:

---------- APA ----------
Martínez, N.G. & Priestley, H.A. (1998) . On Priestley Spaces of Lattice-Ordered Algebraic Structures. Order, 15(4), 297-323.
http://dx.doi.org/10.1023/A:1006224930256
---------- CHICAGO ----------
Martínez, N.G., Priestley, H.A. "On Priestley Spaces of Lattice-Ordered Algebraic Structures" . Order 15, no. 4 (1998) : 297-323.
http://dx.doi.org/10.1023/A:1006224930256
---------- MLA ----------
Martínez, N.G., Priestley, H.A. "On Priestley Spaces of Lattice-Ordered Algebraic Structures" . Order, vol. 15, no. 4, 1998, pp. 297-323.
http://dx.doi.org/10.1023/A:1006224930256
---------- VANCOUVER ----------
Martínez, N.G., Priestley, H.A. On Priestley Spaces of Lattice-Ordered Algebraic Structures. Order. 1998;15(4):297-323.
http://dx.doi.org/10.1023/A:1006224930256