A simplified duality for implicative lattices and l-groups

A topological duality is presented for a wide class of lattice-ordered structures including lattice-ordered groups. In this new approach, which simplifies considerably previous results of the author, the dual space is obtained by endowing the Priestley space of the underlying lattice with two binary...

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Autor principal: Martinez, N.G.
Formato: JOUR
Materias:
Duality
Implicative lattices
Lattice-ordered groups
Priestley spaces
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00393215_v56_n1-2_p185_Martinez
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_00393215_v56_n1-2_p185_Martinez
record_format dspace
spelling todo:paper_00393215_v56_n1-2_p185_Martinez2023-10-03T14:49:40Z A simplified duality for implicative lattices and l-groups Martinez, N.G. Duality Implicative lattices Lattice-ordered groups Priestley spaces A topological duality is presented for a wide class of lattice-ordered structures including lattice-ordered groups. In this new approach, which simplifies considerably previous results of the author, the dual space is obtained by endowing the Priestley space of the underlying lattice with two binary functions, linked by set-theoretical complement and acting as symmetrical partners. In the particular case of l-groups, one of these functions is the usual product of sets and the axiomatization of the dual space is given by very simple first-order sentences, saying essentially that both functions are associative and that the space is a residuated semigroup with respect to each of them. © 1996 Kluwer Academic Publishers. Fil:Martinez, 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_00393215_v56_n1-2_p185_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 lattices
Lattice-ordered groups
Priestley spaces
spellingShingle Duality
Implicative lattices
Lattice-ordered groups
Priestley spaces
Martinez, N.G.
A simplified duality for implicative lattices and l-groups
topic_facet Duality
Implicative lattices
Lattice-ordered groups
Priestley spaces
description A topological duality is presented for a wide class of lattice-ordered structures including lattice-ordered groups. In this new approach, which simplifies considerably previous results of the author, the dual space is obtained by endowing the Priestley space of the underlying lattice with two binary functions, linked by set-theoretical complement and acting as symmetrical partners. In the particular case of l-groups, one of these functions is the usual product of sets and the axiomatization of the dual space is given by very simple first-order sentences, saying essentially that both functions are associative and that the space is a residuated semigroup with respect to each of them. © 1996 Kluwer Academic Publishers.
format JOUR
author Martinez, N.G.
author_facet Martinez, N.G.
author_sort Martinez, N.G.
title A simplified duality for implicative lattices and l-groups
title_short A simplified duality for implicative lattices and l-groups
title_full A simplified duality for implicative lattices and l-groups
title_fullStr A simplified duality for implicative lattices and l-groups
title_full_unstemmed A simplified duality for implicative lattices and l-groups
title_sort simplified duality for implicative lattices and l-groups
url http://hdl.handle.net/20.500.12110/paper_00393215_v56_n1-2_p185_Martinez
work_keys_str_mv AT martinezng asimplifieddualityforimplicativelatticesandlgroups
AT martinezng simplifieddualityforimplicativelatticesandlgroups
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