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, Alejandro Gustavo
Publicado:	1996
Materias:	Bounded distributive lattices Closure operators Congruence relations Join-homomorphisms Lattice homomorphisms Priestley relations Priestley spaces Quantifiers Varieties
Acceso en línea:	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00393215_v56_n1-2_p205_Petrovich 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	paper:paper_00393215_v56_n1-2_p205_Petrovich
record_format	dspace
spelling	paper:paper_00393215_v56_n1-2_p205_Petrovich2023-06-08T15:03:28Z Distributive lattices with an operator Petrovich, Alejandro Gustavo 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. 1996 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00393215_v56_n1-2_p205_Petrovich 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, Alejandro Gustavo 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.
author	Petrovich, Alejandro Gustavo
author_facet	Petrovich, Alejandro Gustavo
author_sort	Petrovich, Alejandro Gustavo
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
publishDate	1996
url	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00393215_v56_n1-2_p205_Petrovich http://hdl.handle.net/20.500.12110/paper_00393215_v56_n1-2_p205_Petrovich
work_keys_str_mv	AT petrovichalejandrogustavo distributivelatticeswithanoperator
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Distributive lattices with an operator

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