Distributive lattices with an operator

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...

Descripción completa

Guardado en:
Detalles Bibliográficos
Autor principal: Petrovich, A.
Formato: Capítulo de libro
Lenguaje:Inglés
Publicado: Springer Netherlands 1996
Acceso en línea:Registro en Scopus
DOI
Handle
Registro en la Biblioteca Digital
Aporte de:Registro referencial: Solicitar el recurso aquí
LEADER 04448caa a22005297a 4500
001 PAPER-3389
003 AR-BaUEN
005 20230518203251.0
008 190411s1996 xx ||||fo|||| 00| 0 eng|d
024 7 |2 scopus  |a 2-s2.0-0039715876 
040 |a Scopus  |b spa  |c AR-BaUEN  |d AR-BaUEN 
100 1 |a Petrovich, A. 
245 1 0 |a Distributive lattices with an operator 
260 |b Springer Netherlands  |c 1996 
270 1 0 |m Petrovich, A.; Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Ciudad Universitaria, 1428 Buenos Aires, Argentina; email: apetrov@mate.dm.uba.ar 
506 |2 openaire  |e Política editorial 
504 |a Blok, W.J., Dwinger, P.H., Equational classes of closure algebras (1975) Ind. Math., 37, pp. 189-198 
504 |a 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 
504 |a Cignoli, R., Lafalce, S., Petrovich, A., Remarks on Priestley duality for distributive lattices (1991) Order, 8, pp. 299-315 
504 |a Cignoli, R., Quantifiers on distributive lattices (1991) Discrete Math., 96, pp. 183-197 
504 |a Goldblatt, R., Varieties of Complex algebras (1989) Ann. Pure Appl. Logic., 44, pp. 173-242 
504 |a McKinsey, J.C.C., Tarski, A., The algebra of topology (1944) Ann. of Math., 45, pp. 141-191 
504 |a Petrovich, A., Monadic de Morgan Algebras, , to appear 
504 |a Priestley, H.A., Representation of distributive lattices by means of ordered Stone spaces (1970) Bull. London Math. Soc., 2, pp. 186-190 
504 |a Priestley, H.A., Ordered topological spaces and the representation of distributive lattices (1972) Proc. London Math. Soc., 3, pp. 507-530 
504 |a Priestley, H.A., Stone lattices: A topological approach (1974) Fund. Math., 84, pp. 127-143 
504 |a Priestley, H.A., Ordered sets and duality for distributive lattices (1984) Ann. Discrete Math., 23, pp. 39-60 
504 |a Rasiowa, H., Sikorski, R., (1963) The Mathematics of Metamathematics, , Warszawa 
520 3 |a 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.  |l eng 
593 |a Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Ciudad Universitaria, 1428 Buenos Aires, Argentina 
690 1 0 |a BOUNDED DISTRIBUTIVE LATTICES 
690 1 0 |a CLOSURE OPERATORS 
690 1 0 |a CONGRUENCE RELATIONS 
690 1 0 |a JOIN-HOMOMORPHISMS 
690 1 0 |a LATTICE HOMOMORPHISMS 
690 1 0 |a PRIESTLEY RELATIONS 
690 1 0 |a PRIESTLEY SPACES 
690 1 0 |a QUANTIFIERS 
690 1 0 |a VARIETIES 
773 0 |d Springer Netherlands, 1996  |g v. 56  |h pp. 205-224  |k n. 1-2  |p Stud. Logica  |x 00393215  |w (AR-BaUEN)CENRE-365  |t Studia Logica 
856 4 1 |u https://www.scopus.com/inward/record.uri?eid=2-s2.0-0039715876&doi=10.1007%2fBF00370147&partnerID=40&md5=15ba536a1082aad911d4008274136ff2  |y Registro en Scopus 
856 4 0 |u https://doi.org/10.1007/BF00370147  |y DOI 
856 4 0 |u https://hdl.handle.net/20.500.12110/paper_00393215_v56_n1-2_p205_Petrovich  |y Handle 
856 4 0 |u https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00393215_v56_n1-2_p205_Petrovich  |y Registro en la Biblioteca Digital 
961 |a paper_00393215_v56_n1-2_p205_Petrovich  |b paper  |c PE 
962 |a info:eu-repo/semantics/article  |a info:ar-repo/semantics/artículo  |b info:eu-repo/semantics/publishedVersion 
999 |c 64342