Artículo
Petrovich, A. "Equations in the theory of Q-distributive lattices" (1997) Discrete Mathematics. 175(1-3):211-219
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Abstract:
A Q-distributive lattice is an algebra (L, ∨, ∧, ∇, 0, 1) of type (2, 2, 1, 0, 0) such that (L, ∨, ∧, 0, 1) is a bounded distributive lattice and ∇ satisfies the equations ∇0 = 0, x ∧ ∇x = x, ∇(x ∨ y) = ∇x ∨ ∇y and ∇(x ∧ ∇y) = ∇x ∧ ∇y. The aim of this paper is to find, for each proper subvariety of the variety of Q-distributive lattices, an equation which determines it, relatively to the whole variety, as well as to give a characterization of the minimum number of variables needed in such equation.
Registro:
| Documento: | Artículo |
| Título: | Equations in the theory of Q-distributive lattices |
| Autor: | Petrovich, A. |
| Filiación: | Departamento de Matemática, Fac. de Ciencias Exactas y Naturales, Ciudad Universitaria, 1428 Buenos Aires, Argentina |
| Año: | 1997 |
| Volumen: | 175 |
| Número: | 1-3 |
| Página de inicio: | 211 |
| Página de fin: | 219 |
| DOI: | http://dx.doi.org/10.1016/S0012-365X(96)00151-3 |
| Título revista: | Discrete Mathematics |
| Título revista abreviado: | Discrete Math |
| ISSN: | 0012365X |
| CODEN: | DSMHA |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0012365X_v175_n1-3_p211_Petrovich |
Referencias:
- Burris, S., Sankappanavar, H.P., (1981) A Course in Universal Algebra, , Springer, New York
- Cignoli, R., Quantifiers on distributive lattices (1991) Discrete Math., 96, pp. 183-197
- Cignoli, R., Petrovich, A., On the Minimum Number of Variables Needed to Characterize Some Subvarieties of a Congruence Distributive Variety, , to appear
- Day, A., Splitting algebras and a weak notion of projectivity (1975) Algebra Universalis, 5, pp. 153-162
- Jonsson, B., Algebras whose congruence lattices are distributive (1967) Math. Scand., 21, pp. 110-121
- Lucas, Th., Equations in the theory of monadic algebras (1972) Proc. Amer. Math. Soc., 1 (31), pp. 239-244
- McKenzie, R., Equational bases and non-modular lattice varieties (1972) Trans. Amer. Math. Soc., 174, pp. 1-43
- Monk, J.D., On equational classes of algebraic versions of logic. I (1970) Math. Scand., 27, pp. 53-71
Citas:
---------- APA ----------
(1997) . Equations in the theory of Q-distributive lattices. Discrete Mathematics, 175(1-3), 211-219.http://dx.doi.org/10.1016/S0012-365X(96)00151-3
---------- CHICAGO ----------
Petrovich, A. "Equations in the theory of Q-distributive lattices" . Discrete Mathematics 175, no. 1-3 (1997) : 211-219.http://dx.doi.org/10.1016/S0012-365X(96)00151-3
---------- MLA ----------
Petrovich, A. "Equations in the theory of Q-distributive lattices" . Discrete Mathematics, vol. 175, no. 1-3, 1997, pp. 211-219.http://dx.doi.org/10.1016/S0012-365X(96)00151-3
---------- VANCOUVER ----------
Petrovich, A. Equations in the theory of Q-distributive lattices. Discrete Math. 1997;175(1-3):211-219.http://dx.doi.org/10.1016/S0012-365X(96)00151-3
