On Priestley Spaces of Lattice-Ordered Algebraic Structures

The laws defining many important varieties of lattice-ordered algebras, such as linear Heyting algebras, MV-algebras and l-groups, can be cast in a form which allows dual representations to be derived in a very direct, and semi-automatic, way. This is achieved by developing a new duality theory for...

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Autores principales: Martínez, N.G., Priestley, H.A.
Formato: JOUR
Materias:
Duality
Implicative lattice
Lattice-ordered group
Priestley space
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_01678094_v15_n4_p297_Martinez
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_01678094_v15_n4_p297_Martinez
record_format dspace
spelling todo:paper_01678094_v15_n4_p297_Martinez2023-10-03T15:05:22Z On Priestley Spaces of Lattice-Ordered Algebraic Structures Martínez, N.G. Priestley, H.A. Duality Implicative lattice Lattice-ordered group Priestley space The laws defining many important varieties of lattice-ordered algebras, such as linear Heyting algebras, MV-algebras and l-groups, can be cast in a form which allows dual representations to be derived in a very direct, and semi-automatic, way. This is achieved by developing a new duality theory for implicative lattices, which encompass all the varieries above. The approach focuses on distinguished subsets of the prime lattice filters of an implicative lattice, ordered as usual by inclusion. A decomposition theorem is proved, and the extent to which the order on the prime lattice filters determines the implicative structure is thereby revealed. Fil:Martínez, N.G. 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_01678094_v15_n4_p297_Martinez
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Duality
Implicative lattice
Lattice-ordered group
Priestley space
spellingShingle Duality
Implicative lattice
Lattice-ordered group
Priestley space
Martínez, N.G.
Priestley, H.A.
On Priestley Spaces of Lattice-Ordered Algebraic Structures
topic_facet Duality
Implicative lattice
Lattice-ordered group
Priestley space
description The laws defining many important varieties of lattice-ordered algebras, such as linear Heyting algebras, MV-algebras and l-groups, can be cast in a form which allows dual representations to be derived in a very direct, and semi-automatic, way. This is achieved by developing a new duality theory for implicative lattices, which encompass all the varieries above. The approach focuses on distinguished subsets of the prime lattice filters of an implicative lattice, ordered as usual by inclusion. A decomposition theorem is proved, and the extent to which the order on the prime lattice filters determines the implicative structure is thereby revealed.
format JOUR
author Martínez, N.G.
Priestley, H.A.
author_facet Martínez, N.G.
Priestley, H.A.
author_sort Martínez, N.G.
title On Priestley Spaces of Lattice-Ordered Algebraic Structures
title_short On Priestley Spaces of Lattice-Ordered Algebraic Structures
title_full On Priestley Spaces of Lattice-Ordered Algebraic Structures
title_fullStr On Priestley Spaces of Lattice-Ordered Algebraic Structures
title_full_unstemmed On Priestley Spaces of Lattice-Ordered Algebraic Structures
title_sort on priestley spaces of lattice-ordered algebraic structures
url http://hdl.handle.net/20.500.12110/paper_01678094_v15_n4_p297_Martinez
work_keys_str_mv AT martinezng onpriestleyspacesoflatticeorderedalgebraicstructures
AT priestleyha onpriestleyspacesoflatticeorderedalgebraicstructures
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