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
CIC Digital (CICBA)
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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network_name_str CIC Digital (CICBA)
spelling 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
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info:ar-repo/semantics/articulo
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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
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info:eu-repo/semantics/altIdentifier/issn/0002-5240
info:eu-repo/semantics/altIdentifier/issn/1420-8911
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instname_str Comisión de Investigaciones Científicas de la Provincia de Buenos Aires
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