A representation theorem for integral rigs and its applications to residuated lattices

Autores
Castiglioni, José Luis; Menni, Matías; Zuluaga Botero, William Javier
Año de publicación
2016
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We generalize the Dubuc–Poveda representation theorem for MV-algebras so that it applies to other algebraic categories of residuated join-semilattices. In particular, as a corollary, we obtain a representation result for pre-linear residuated join-semilattices in terms of totally ordered fibers. The main result is analogous to the Zariski representation of (commutative) rings and it is proved using tools from topos theory.
Fil: Castiglioni, José Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina. Universidad Nacional de La Plata; Argentina
Fil: Menni, Matías. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina. Universidad Nacional de La Plata; Argentina
Fil: Zuluaga Botero, William Javier. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina. Universidad Nacional de La Plata; Argentina
Materia
Sheaves
Integral Rigs
Really Local Objects
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/54815
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/54815
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network_name_str CONICET Digital (CONICET)
spelling A representation theorem for integral rigs and its applications to residuated latticesCastiglioni, José LuisMenni, MatíasZuluaga Botero, William JavierSheavesIntegral RigsReally Local Objectshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We generalize the Dubuc–Poveda representation theorem for MV-algebras so that it applies to other algebraic categories of residuated join-semilattices. In particular, as a corollary, we obtain a representation result for pre-linear residuated join-semilattices in terms of totally ordered fibers. The main result is analogous to the Zariski representation of (commutative) rings and it is proved using tools from topos theory.Fil: Castiglioni, José Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina. Universidad Nacional de La Plata; ArgentinaFil: Menni, Matías. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina. Universidad Nacional de La Plata; ArgentinaFil: Zuluaga Botero, William Javier. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina. Universidad Nacional de La Plata; ArgentinaElsevier Science2016-05info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/54815Castiglioni, José Luis; Menni, Matías; Zuluaga Botero, William Javier; A representation theorem for integral rigs and its applications to residuated lattices; Elsevier Science; Journal Of Pure And Applied Algebra; 220; 10; 5-2016; 3533-35660022-4049CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0022404916300226info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jpaa.2016.04.014info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:42:18Zoai:ri.conicet.gov.ar:11336/54815instacron: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 09:42:19.048CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A representation theorem for integral rigs and its applications to residuated lattices
title A representation theorem for integral rigs and its applications to residuated lattices
spellingShingle A representation theorem for integral rigs and its applications to residuated lattices
Castiglioni, José Luis
Sheaves
Integral Rigs
Really Local Objects
title_short A representation theorem for integral rigs and its applications to residuated lattices
title_full A representation theorem for integral rigs and its applications to residuated lattices
title_fullStr A representation theorem for integral rigs and its applications to residuated lattices
title_full_unstemmed A representation theorem for integral rigs and its applications to residuated lattices
title_sort A representation theorem for integral rigs and its applications to residuated lattices
dc.creator.none.fl_str_mv Castiglioni, José Luis
Menni, Matías
Zuluaga Botero, William Javier
author Castiglioni, José Luis
author_facet Castiglioni, José Luis
Menni, Matías
Zuluaga Botero, William Javier
author_role author
author2 Menni, Matías
Zuluaga Botero, William Javier
author2_role author
author
dc.subject.none.fl_str_mv Sheaves
Integral Rigs
Really Local Objects
topic Sheaves
Integral Rigs
Really Local Objects
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We generalize the Dubuc–Poveda representation theorem for MV-algebras so that it applies to other algebraic categories of residuated join-semilattices. In particular, as a corollary, we obtain a representation result for pre-linear residuated join-semilattices in terms of totally ordered fibers. The main result is analogous to the Zariski representation of (commutative) rings and it is proved using tools from topos theory.
Fil: Castiglioni, José Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina. Universidad Nacional de La Plata; Argentina
Fil: Menni, Matías. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina. Universidad Nacional de La Plata; Argentina
Fil: Zuluaga Botero, William Javier. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina. Universidad Nacional de La Plata; Argentina
description We generalize the Dubuc–Poveda representation theorem for MV-algebras so that it applies to other algebraic categories of residuated join-semilattices. In particular, as a corollary, we obtain a representation result for pre-linear residuated join-semilattices in terms of totally ordered fibers. The main result is analogous to the Zariski representation of (commutative) rings and it is proved using tools from topos theory.
publishDate 2016
dc.date.none.fl_str_mv 2016-05
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/11336/54815
Castiglioni, José Luis; Menni, Matías; Zuluaga Botero, William Javier; A representation theorem for integral rigs and its applications to residuated lattices; Elsevier Science; Journal Of Pure And Applied Algebra; 220; 10; 5-2016; 3533-3566
0022-4049
CONICET Digital
CONICET
url http://hdl.handle.net/11336/54815
identifier_str_mv Castiglioni, José Luis; Menni, Matías; Zuluaga Botero, William Javier; A representation theorem for integral rigs and its applications to residuated lattices; Elsevier Science; Journal Of Pure And Applied Algebra; 220; 10; 5-2016; 3533-3566
0022-4049
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0022404916300226
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jpaa.2016.04.014
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier Science
publisher.none.fl_str_mv Elsevier Science
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 13.070432

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