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...

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Autor principal: Petrovich, A.
Formato: JOUR
Materias:
Bounded distributive lattices
Closure operators
Congruence relations
Join-homomorphisms
Lattice homomorphisms
Priestley relations
Priestley spaces
Quantifiers
Varieties
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00393215_v56_n1-2_p205_Petrovich
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_00393215_v56_n1-2_p205_Petrovich
record_format dspace
spelling todo:paper_00393215_v56_n1-2_p205_Petrovich2023-10-03T14:49:41Z Distributive lattices with an operator Petrovich, A. Bounded distributive lattices Closure operators Congruence relations Join-homomorphisms Lattice homomorphisms Priestley relations Priestley spaces Quantifiers Varieties 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. Fil:Petrovich, A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00393215_v56_n1-2_p205_Petrovich
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Bounded distributive lattices
Closure operators
Congruence relations
Join-homomorphisms
Lattice homomorphisms
Priestley relations
Priestley spaces
Quantifiers
Varieties
spellingShingle Bounded distributive lattices
Closure operators
Congruence relations
Join-homomorphisms
Lattice homomorphisms
Priestley relations
Priestley spaces
Quantifiers
Varieties
Petrovich, A.
Distributive lattices with an operator
topic_facet Bounded distributive lattices
Closure operators
Congruence relations
Join-homomorphisms
Lattice homomorphisms
Priestley relations
Priestley spaces
Quantifiers
Varieties
description 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.
format JOUR
author Petrovich, A.
author_facet Petrovich, A.
author_sort Petrovich, A.
title Distributive lattices with an operator
title_short Distributive lattices with an operator
title_full Distributive lattices with an operator
title_fullStr Distributive lattices with an operator
title_full_unstemmed Distributive lattices with an operator
title_sort distributive lattices with an operator
url http://hdl.handle.net/20.500.12110/paper_00393215_v56_n1-2_p205_Petrovich
work_keys_str_mv AT petrovicha distributivelatticeswithanoperator
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