Hilbert Algebras with Hilbert-Galois Connections II

Autores
Celani, Sergio Arturo; Montagie, Daniela
Año de publicación
2024
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Hilbert algebra with a Hilbert-Galois connection, or HilGC-algebra, is a triple (A, f, g) where A is a Hilbert algebra, and f and g are unary maps on A such that f(a) ≤ b iff a ≤ g(b), and g(a → b) ≤ g(a) → g(b) for all a, b ∈ A. In this paper, we are going to prove that some varieties of HilGC-algebras are characterized by first-order conditions defined in the dual space and that these varieties are canonical. Additionally, we will also study and characterize the congruences of an HilGC-algebra through specific closed subsets of the dual space. This characterization will be applied to determine the simple algebras and subdirectly irreducible HilGC-algebras.
Fil: Celani, Sergio Arturo. Universidad Nacional del Centro de la Provincia de Buenos Aires. Facultad de Ciencias Exactas. Núcleo Consolidado de Matemática Pura y Aplicada; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Tandil; Argentina
Fil: Montagie, Daniela. Universidad Nacional del Comahue; Argentina
Materia
HILBERT ALGEBRAS
MODAL OPERATORS
GALOIS CONNECTION
CANONICAL VARIETIES
CONGRUENCES
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/256158
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/256158
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Hilbert Algebras with Hilbert-Galois Connections IICelani, Sergio ArturoMontagie, DanielaHILBERT ALGEBRASMODAL OPERATORSGALOIS CONNECTIONCANONICAL VARIETIESCONGRUENCEShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Hilbert algebra with a Hilbert-Galois connection, or HilGC-algebra, is a triple (A, f, g) where A is a Hilbert algebra, and f and g are unary maps on A such that f(a) ≤ b iff a ≤ g(b), and g(a → b) ≤ g(a) → g(b) for all a, b ∈ A. In this paper, we are going to prove that some varieties of HilGC-algebras are characterized by first-order conditions defined in the dual space and that these varieties are canonical. Additionally, we will also study and characterize the congruences of an HilGC-algebra through specific closed subsets of the dual space. This characterization will be applied to determine the simple algebras and subdirectly irreducible HilGC-algebras.Fil: Celani, Sergio Arturo. Universidad Nacional del Centro de la Provincia de Buenos Aires. Facultad de Ciencias Exactas. Núcleo Consolidado de Matemática Pura y Aplicada; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Tandil; ArgentinaFil: Montagie, Daniela. Universidad Nacional del Comahue; ArgentinaLodz University2024-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/256158Celani, Sergio Arturo; Montagie, Daniela; Hilbert Algebras with Hilbert-Galois Connections II; Lodz University; Bulletin Of The Section Of Logic; 53; 4; 12-2024; 535-5540138-0680CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://czasopisma.uni.lodz.pl/bulletin/article/view/23268info:eu-repo/semantics/altIdentifier/doi/10.18778/0138-0680.2024.17info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:15:15Zoai:ri.conicet.gov.ar:11336/256158instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 10:15:15.362CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Hilbert Algebras with Hilbert-Galois Connections II
title Hilbert Algebras with Hilbert-Galois Connections II
spellingShingle Hilbert Algebras with Hilbert-Galois Connections II
Celani, Sergio Arturo
HILBERT ALGEBRAS
MODAL OPERATORS
GALOIS CONNECTION
CANONICAL VARIETIES
CONGRUENCES
title_short Hilbert Algebras with Hilbert-Galois Connections II
title_full Hilbert Algebras with Hilbert-Galois Connections II
title_fullStr Hilbert Algebras with Hilbert-Galois Connections II
title_full_unstemmed Hilbert Algebras with Hilbert-Galois Connections II
title_sort Hilbert Algebras with Hilbert-Galois Connections II
dc.creator.none.fl_str_mv Celani, Sergio Arturo
Montagie, Daniela
author Celani, Sergio Arturo
author_facet Celani, Sergio Arturo
Montagie, Daniela
author_role author
author2 Montagie, Daniela
author2_role author
dc.subject.none.fl_str_mv HILBERT ALGEBRAS
MODAL OPERATORS
GALOIS CONNECTION
CANONICAL VARIETIES
CONGRUENCES
topic HILBERT ALGEBRAS
MODAL OPERATORS
GALOIS CONNECTION
CANONICAL VARIETIES
CONGRUENCES
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Hilbert algebra with a Hilbert-Galois connection, or HilGC-algebra, is a triple (A, f, g) where A is a Hilbert algebra, and f and g are unary maps on A such that f(a) ≤ b iff a ≤ g(b), and g(a → b) ≤ g(a) → g(b) for all a, b ∈ A. In this paper, we are going to prove that some varieties of HilGC-algebras are characterized by first-order conditions defined in the dual space and that these varieties are canonical. Additionally, we will also study and characterize the congruences of an HilGC-algebra through specific closed subsets of the dual space. This characterization will be applied to determine the simple algebras and subdirectly irreducible HilGC-algebras.
Fil: Celani, Sergio Arturo. Universidad Nacional del Centro de la Provincia de Buenos Aires. Facultad de Ciencias Exactas. Núcleo Consolidado de Matemática Pura y Aplicada; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Tandil; Argentina
Fil: Montagie, Daniela. Universidad Nacional del Comahue; Argentina
description Hilbert algebra with a Hilbert-Galois connection, or HilGC-algebra, is a triple (A, f, g) where A is a Hilbert algebra, and f and g are unary maps on A such that f(a) ≤ b iff a ≤ g(b), and g(a → b) ≤ g(a) → g(b) for all a, b ∈ A. In this paper, we are going to prove that some varieties of HilGC-algebras are characterized by first-order conditions defined in the dual space and that these varieties are canonical. Additionally, we will also study and characterize the congruences of an HilGC-algebra through specific closed subsets of the dual space. This characterization will be applied to determine the simple algebras and subdirectly irreducible HilGC-algebras.
publishDate 2024
dc.date.none.fl_str_mv 2024-12
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/256158
Celani, Sergio Arturo; Montagie, Daniela; Hilbert Algebras with Hilbert-Galois Connections II; Lodz University; Bulletin Of The Section Of Logic; 53; 4; 12-2024; 535-554
0138-0680
CONICET Digital
CONICET
url http://hdl.handle.net/11336/256158
identifier_str_mv Celani, Sergio Arturo; Montagie, Daniela; Hilbert Algebras with Hilbert-Galois Connections II; Lodz University; Bulletin Of The Section Of Logic; 53; 4; 12-2024; 535-554
0138-0680
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://czasopisma.uni.lodz.pl/bulletin/article/view/23268
info:eu-repo/semantics/altIdentifier/doi/10.18778/0138-0680.2024.17
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Lodz University
publisher.none.fl_str_mv Lodz University
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.069144

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