A new categorical equivalence for stone algebras

Autores
Calomino, Ismael; Pelaitay, Gustavo Andrés
Año de publicación
2025
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The aim of this paper is to give a categorical equivalence for Stone algebras. We introduce the variety of Stone-Kleene algebras with intuitionistic negation, or Stone KAN-algebras for short, and explore Kalman's construction for Stone algebras. We examine the centered algebras within this new variety and prove that the category of Stone algebras is equivalent to the category of centered Stone KAN-algebras. Moreover, inspired by Monteiro's construction for Nelson algebras, we propose a method to construct a centered Stone KAN-algebra from a given Stone KAN-algebra and show the connection between Kalman's construction and Monteiro's construction.
Fil: Calomino, Ismael. Universidad Católica de Ávila; España
Fil: Pelaitay, Gustavo Andrés. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de San Juan. Facultad de Filosofía, Humanidades y Artes. Instituto de Ciencias Básicas; Argentina
Materia
KLEENE ALGEBRA
PSEUDOCOMPLEMENTED DISTRIBUTIVE LATTICE
STONE IDENTITY
INTUITIONISTIC NEGATION
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:11336/280147
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/280147
network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling A new categorical equivalence for stone algebrasCalomino, IsmaelPelaitay, Gustavo AndrésKLEENE ALGEBRAPSEUDOCOMPLEMENTED DISTRIBUTIVE LATTICESTONE IDENTITYINTUITIONISTIC NEGATIONhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1The aim of this paper is to give a categorical equivalence for Stone algebras. We introduce the variety of Stone-Kleene algebras with intuitionistic negation, or Stone KAN-algebras for short, and explore Kalman's construction for Stone algebras. We examine the centered algebras within this new variety and prove that the category of Stone algebras is equivalent to the category of centered Stone KAN-algebras. Moreover, inspired by Monteiro's construction for Nelson algebras, we propose a method to construct a centered Stone KAN-algebra from a given Stone KAN-algebra and show the connection between Kalman's construction and Monteiro's construction.Fil: Calomino, Ismael. Universidad Católica de Ávila; EspañaFil: Pelaitay, Gustavo Andrés. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de San Juan. Facultad de Filosofía, Humanidades y Artes. Instituto de Ciencias Básicas; ArgentinaVersita2025-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/280147Calomino, Ismael; Pelaitay, Gustavo Andrés; A new categorical equivalence for stone algebras; Versita; Mathematica Slovaca; 75; 6; 12-2025; 1275-12920139-9918CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.degruyterbrill.com/document/doi/10.1515/ms-2025-0093/htmlinfo:eu-repo/semantics/altIdentifier/doi/10.1515/ms-2025-0093info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2026-02-26T10:21:14Zoai:ri.conicet.gov.ar:11336/280147instacron: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:34982026-02-26 10:21:15.12CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A new categorical equivalence for stone algebras
title A new categorical equivalence for stone algebras
spellingShingle A new categorical equivalence for stone algebras
Calomino, Ismael
KLEENE ALGEBRA
PSEUDOCOMPLEMENTED DISTRIBUTIVE LATTICE
STONE IDENTITY
INTUITIONISTIC NEGATION
title_short A new categorical equivalence for stone algebras
title_full A new categorical equivalence for stone algebras
title_fullStr A new categorical equivalence for stone algebras
title_full_unstemmed A new categorical equivalence for stone algebras
title_sort A new categorical equivalence for stone algebras
dc.creator.none.fl_str_mv Calomino, Ismael
Pelaitay, Gustavo Andrés
author Calomino, Ismael
author_facet Calomino, Ismael
Pelaitay, Gustavo Andrés
author_role author
author2 Pelaitay, Gustavo Andrés
author2_role author
dc.subject.none.fl_str_mv KLEENE ALGEBRA
PSEUDOCOMPLEMENTED DISTRIBUTIVE LATTICE
STONE IDENTITY
INTUITIONISTIC NEGATION
topic KLEENE ALGEBRA
PSEUDOCOMPLEMENTED DISTRIBUTIVE LATTICE
STONE IDENTITY
INTUITIONISTIC NEGATION
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv The aim of this paper is to give a categorical equivalence for Stone algebras. We introduce the variety of Stone-Kleene algebras with intuitionistic negation, or Stone KAN-algebras for short, and explore Kalman's construction for Stone algebras. We examine the centered algebras within this new variety and prove that the category of Stone algebras is equivalent to the category of centered Stone KAN-algebras. Moreover, inspired by Monteiro's construction for Nelson algebras, we propose a method to construct a centered Stone KAN-algebra from a given Stone KAN-algebra and show the connection between Kalman's construction and Monteiro's construction.
Fil: Calomino, Ismael. Universidad Católica de Ávila; España
Fil: Pelaitay, Gustavo Andrés. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de San Juan. Facultad de Filosofía, Humanidades y Artes. Instituto de Ciencias Básicas; Argentina
description The aim of this paper is to give a categorical equivalence for Stone algebras. We introduce the variety of Stone-Kleene algebras with intuitionistic negation, or Stone KAN-algebras for short, and explore Kalman's construction for Stone algebras. We examine the centered algebras within this new variety and prove that the category of Stone algebras is equivalent to the category of centered Stone KAN-algebras. Moreover, inspired by Monteiro's construction for Nelson algebras, we propose a method to construct a centered Stone KAN-algebra from a given Stone KAN-algebra and show the connection between Kalman's construction and Monteiro's construction.
publishDate 2025
dc.date.none.fl_str_mv 2025-12
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/11336/280147
Calomino, Ismael; Pelaitay, Gustavo Andrés; A new categorical equivalence for stone algebras; Versita; Mathematica Slovaca; 75; 6; 12-2025; 1275-1292
0139-9918
CONICET Digital
CONICET
url http://hdl.handle.net/11336/280147
identifier_str_mv Calomino, Ismael; Pelaitay, Gustavo Andrés; A new categorical equivalence for stone algebras; Versita; Mathematica Slovaca; 75; 6; 12-2025; 1275-1292
0139-9918
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://www.degruyterbrill.com/document/doi/10.1515/ms-2025-0093/html
info:eu-repo/semantics/altIdentifier/doi/10.1515/ms-2025-0093
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 Versita
publisher.none.fl_str_mv Versita
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 13.176822

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