Dualities for Subresiduated latttices
- Autores
- Celani, Sergio; Nagy, Agustín Leonel; San Martín, Hernán
- Año de publicación
- 2021
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión aceptada
- Descripción
- A subresiduated lattice is a pair (A,D), where A is a bounded distributive lattice, D is a bounded sublattice of A and for every a, b ∈ A there is c ∈ D such that for all d ∈ D, d ∧ a ≤ b if and only if d ≤ c. This c is denoted by a → b. This pair can be regarded as an algebra ⟨A, ∧, ∨,→, 0, 1⟩ of type (2, 2, 2, 0, 0) where D = {a ∈ A : 1 → a = a}. The class of subresiduated lattices is a variety which properly contains to the variety of Heyting algebras. In this paper we present dual equivalences for the algebraic category of subresiduated lattices. More precisely, we develop a spectral style duality and a bitopological style duality for this algebraic category. Finally we study the connections of these results with a known Priestley style duality for the algebraic category of subresiduated lattices.
- Materia
-
Matemáticas
Spectral duality
Strict implication - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- http://creativecommons.org/licenses/by-nc/4.0/
- Repositorio
- Institución
- Comisión de Investigaciones Científicas de la Provincia de Buenos Aires
- OAI Identificador
- oai:digital.cic.gba.gob.ar:11746/11376
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Dualities for Subresiduated lattticesCelani, SergioNagy, Agustín LeonelSan Martín, HernánMatemáticasSpectral dualityStrict implicationA subresiduated lattice is a pair (A,D), where A is a bounded distributive lattice, D is a bounded sublattice of A and for every a, b ∈ A there is c ∈ D such that for all d ∈ D, d ∧ a ≤ b if and only if d ≤ c. This c is denoted by a → b. This pair can be regarded as an algebra ⟨A, ∧, ∨,→, 0, 1⟩ of type (2, 2, 2, 0, 0) where D = {a ∈ A : 1 → a = a}. The class of subresiduated lattices is a variety which properly contains to the variety of Heyting algebras. In this paper we present dual equivalences for the algebraic category of subresiduated lattices. More precisely, we develop a spectral style duality and a bitopological style duality for this algebraic category. Finally we study the connections of these results with a known Priestley style duality for the algebraic category of subresiduated lattices.2021info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfhttps://digital.cic.gba.gob.ar/handle/11746/11376enginfo:eu-repo/semantics/altIdentifier/doi/10.1007/s00012-021-00752-3info:eu-repo/semantics/altIdentifier/issn/0002-5240info:eu-repo/semantics/altIdentifier/issn/1420-8911info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc/4.0/reponame:CIC Digital (CICBA)instname:Comisión de Investigaciones Científicas de la Provincia de Buenos Airesinstacron:CICBA2025-09-29T13:39:57Zoai:digital.cic.gba.gob.ar:11746/11376Institucionalhttp://digital.cic.gba.gob.arOrganismo científico-tecnológicoNo correspondehttp://digital.cic.gba.gob.ar/oai/snrdmarisa.degiusti@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:94412025-09-29 13:39:58.054CIC Digital (CICBA) - Comisión de Investigaciones Científicas de la Provincia de Buenos Airesfalse |
dc.title.none.fl_str_mv |
Dualities for Subresiduated latttices |
title |
Dualities for Subresiduated latttices |
spellingShingle |
Dualities for Subresiduated latttices Celani, Sergio Matemáticas Spectral duality Strict implication |
title_short |
Dualities for Subresiduated latttices |
title_full |
Dualities for Subresiduated latttices |
title_fullStr |
Dualities for Subresiduated latttices |
title_full_unstemmed |
Dualities for Subresiduated latttices |
title_sort |
Dualities for Subresiduated latttices |
dc.creator.none.fl_str_mv |
Celani, Sergio Nagy, Agustín Leonel San Martín, Hernán |
author |
Celani, Sergio |
author_facet |
Celani, Sergio Nagy, Agustín Leonel San Martín, Hernán |
author_role |
author |
author2 |
Nagy, Agustín Leonel San Martín, Hernán |
author2_role |
author author |
dc.subject.none.fl_str_mv |
Matemáticas Spectral duality Strict implication |
topic |
Matemáticas Spectral duality Strict implication |
dc.description.none.fl_txt_mv |
A subresiduated lattice is a pair (A,D), where A is a bounded distributive lattice, D is a bounded sublattice of A and for every a, b ∈ A there is c ∈ D such that for all d ∈ D, d ∧ a ≤ b if and only if d ≤ c. This c is denoted by a → b. This pair can be regarded as an algebra ⟨A, ∧, ∨,→, 0, 1⟩ of type (2, 2, 2, 0, 0) where D = {a ∈ A : 1 → a = a}. The class of subresiduated lattices is a variety which properly contains to the variety of Heyting algebras. In this paper we present dual equivalences for the algebraic category of subresiduated lattices. More precisely, we develop a spectral style duality and a bitopological style duality for this algebraic category. Finally we study the connections of these results with a known Priestley style duality for the algebraic category of subresiduated lattices. |
description |
A subresiduated lattice is a pair (A,D), where A is a bounded distributive lattice, D is a bounded sublattice of A and for every a, b ∈ A there is c ∈ D such that for all d ∈ D, d ∧ a ≤ b if and only if d ≤ c. This c is denoted by a → b. This pair can be regarded as an algebra ⟨A, ∧, ∨,→, 0, 1⟩ of type (2, 2, 2, 0, 0) where D = {a ∈ A : 1 → a = a}. The class of subresiduated lattices is a variety which properly contains to the variety of Heyting algebras. In this paper we present dual equivalences for the algebraic category of subresiduated lattices. More precisely, we develop a spectral style duality and a bitopological style duality for this algebraic category. Finally we study the connections of these results with a known Priestley style duality for the algebraic category of subresiduated lattices. |
publishDate |
2021 |
dc.date.none.fl_str_mv |
2021 |
dc.type.none.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion http://purl.org/coar/resource_type/c_6501 info:ar-repo/semantics/articulo |
format |
article |
status_str |
acceptedVersion |
dc.identifier.none.fl_str_mv |
https://digital.cic.gba.gob.ar/handle/11746/11376 |
url |
https://digital.cic.gba.gob.ar/handle/11746/11376 |
dc.language.none.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
info:eu-repo/semantics/altIdentifier/doi/10.1007/s00012-021-00752-3 info:eu-repo/semantics/altIdentifier/issn/0002-5240 info:eu-repo/semantics/altIdentifier/issn/1420-8911 |
dc.rights.none.fl_str_mv |
info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by-nc/4.0/ |
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openAccess |
rights_invalid_str_mv |
http://creativecommons.org/licenses/by-nc/4.0/ |
dc.format.none.fl_str_mv |
application/pdf |
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reponame:CIC Digital (CICBA) instname:Comisión de Investigaciones Científicas de la Provincia de Buenos Aires instacron:CICBA |
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Comisión de Investigaciones Científicas de la Provincia de Buenos Aires |
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CIC Digital (CICBA) - Comisión de Investigaciones Científicas de la Provincia de Buenos Aires |
repository.mail.fl_str_mv |
marisa.degiusti@sedici.unlp.edu.ar |
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13.070432 |