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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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 |
_version_ |
1782030837345157120 |