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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Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00393215_v56_n1-2_p185_Martinez http://hdl.handle.net/20.500.12110/paper_00393215_v56_n1-2_p185_Martinez |
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paper:paper_00393215_v56_n1-2_p185_Martinez2023-06-08T15:03:28Z A simplified duality for implicative lattices and l-groups Martínez, Néstor Guillermo 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. 1996 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00393215_v56_n1-2_p185_Martinez 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 Martínez, Néstor Guillermo 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. |
author |
Martínez, Néstor Guillermo |
author_facet |
Martínez, Néstor Guillermo |
author_sort |
Martínez, Néstor Guillermo |
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 |
publishDate |
1996 |
url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00393215_v56_n1-2_p185_Martinez http://hdl.handle.net/20.500.12110/paper_00393215_v56_n1-2_p185_Martinez |
work_keys_str_mv |
AT martineznestorguillermo asimplifieddualityforimplicativelatticesandlgroups AT martineznestorguillermo simplifieddualityforimplicativelatticesandlgroups |
_version_ |
1768545039977283584 |