Artículo
Martinez, N.G. "A simplified duality for implicative lattices and l-groups" (1996) Studia Logica. 56(1-2):185-204
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Abstract:
A topological duality is presented for a wide class of lattice-ordered structures including lattice-ordered groups. In this new approach, which simplifies considerably previous results of the author, the dual space is obtained by endowing the Priestley space of the underlying lattice with two binary functions, linked by set-theoretical complement and acting as symmetrical partners. In the particular case of l-groups, one of these functions is the usual product of sets and the axiomatization of the dual space is given by very simple first-order sentences, saying essentially that both functions are associative and that the space is a residuated semigroup with respect to each of them. © 1996 Kluwer Academic Publishers.
Registro:
| Documento: | Artículo |
| Título: | A simplified duality for implicative lattices and l-groups |
| Autor: | Martinez, N.G. |
| Filiación: | Depto. de MatemáTica, Fac. de Clencias Exactas y Nat., Ciudad Universitaria Pab. I, Buenos Aires, Argentina |
| Palabras clave: | Duality; Implicative lattices; Lattice-ordered groups; Priestley spaces |
| Año: | 1996 |
| Volumen: | 56 |
| Número: | 1-2 |
| Página de inicio: | 185 |
| Página de fin: | 204 |
| DOI: | http://dx.doi.org/10.1007/BF00370146 |
| 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_p185_Martinez |
Referencias:
- Balbes, R., Dwinger, P.H., (1975) Distributive Lattices, , Univ. Miss. Press
- Bigard, A., Groupes et Anneaux Reticules Lecture Notes in Mathematics, 608. , Springer Verlag
- Birkhoff, G., Lattice Theory Third Edition (1967) American Mathematical Society Colloquium Publications, 25
- Cornish, W., Fowler, P., Coproducts of de Morgan algebras (1977) Bull. Austral. Math. Soc., 16, pp. 1-13
- Cornish, W., Fowler, P., Coproducts of Kleene algebras (1978) Bull. Austral. Math. Soc. ser A, 27, pp. 209-320
- Cornish, W., Lattice ordered groups and BCK-algebras (1980) Math. Japonica, 254, pp. 471-476
- Chang, C.C., Algebraic Analysis of many valued logics (1958) Trans. Am. Math. Soc., 88, pp. 467-490
- Davey, B., Werner, H., Dualities and equivalences for varieties of algebras (1983) Colloq. Math. Soc. Janos Bolyai, 33, pp. 101-375. , North-Holland, Amsterdam
- Fuchs, L., (1963) Partially Ordered Algebraic Systems, , Pergamon, Oxford
- Martinez, N.G., The Priestley duality for Wajsberg algebras (1990) Studio Logica, 49, pp. 31-46
- Martinez, N.G., A topological duality for a class of lattice-ordered algebraic structures including l-groups Algebra Universalis, , to appear
- Monteiro, A., Sur les algebres de Heyting symetriques' (1980) Portugaliae Mathematica, 39
- Mundici, D., Interpretation of AF -C*-algebras in Lukasiewicz sentential Calculus (1986) Journal of Functional Analysis, 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) Bull. London. Math.Soc., 3, pp. 507-530
- Stone, M.H., Topological representation of distributive lattices and Brouwerian logics (1937) Casopis Pest. Mat., 67, pp. 1-35
Citas:
---------- APA ----------
(1996) . A simplified duality for implicative lattices and l-groups. Studia Logica, 56(1-2), 185-204.http://dx.doi.org/10.1007/BF00370146
---------- CHICAGO ----------
Martinez, N.G. "A simplified duality for implicative lattices and l-groups" . Studia Logica 56, no. 1-2 (1996) : 185-204.http://dx.doi.org/10.1007/BF00370146
---------- MLA ----------
Martinez, N.G. "A simplified duality for implicative lattices and l-groups" . Studia Logica, vol. 56, no. 1-2, 1996, pp. 185-204.http://dx.doi.org/10.1007/BF00370146
---------- VANCOUVER ----------
Martinez, N.G. A simplified duality for implicative lattices and l-groups. Stud. Logica. 1996;56(1-2):185-204.http://dx.doi.org/10.1007/BF00370146
