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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1998
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01678094_v15_n4_p297_Martinez http://hdl.handle.net/20.500.12110/paper_01678094_v15_n4_p297_Martinez |
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paper:paper_01678094_v15_n4_p297_Martinez2025-07-30T17:55:41Z On Priestley Spaces of Lattice-Ordered Algebraic Structures Martínez, Néstor Guillermo 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. 1998 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01678094_v15_n4_p297_Martinez 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, Néstor Guillermo 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. |
| author |
Martínez, Néstor Guillermo |
| author_facet |
Martínez, Néstor Guillermo |
| author_sort |
Martínez, Néstor Guillermo |
| 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 |
| publishDate |
1998 |
| url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01678094_v15_n4_p297_Martinez http://hdl.handle.net/20.500.12110/paper_01678094_v15_n4_p297_Martinez |
| work_keys_str_mv |
AT martineznestorguillermo onpriestleyspacesoflatticeorderedalgebraicstructures |
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1840328232944009216 |