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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/256158
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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 Técnicas2025-09-03T10:01:30Zoai: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:34982025-09-03 10:01:30.85CONICET 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) |
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CONICET Digital (CONICET) |
instname_str |
Consejo Nacional de Investigaciones Científicas y Técnicas |
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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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1842269700276355072 |
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13.13397 |