Implicative subreducts of MV-algebras: free and weakly projective objects

Autores
Castaño, Diego Nicolás
Año de publicación
2017
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this article, we explore in some detail the free and weakly projective objects of the variety of Łukasiewicz implication algebras (the implicative subreducts of MV-algebras). We review the two already known descriptions of finitely generated free algebras, giving new insights into their structure and their connection, as well as providing new proofs of the characterizations. We give a representation theorem for weakly projective algebras as algebras of certain McNaughton functions restricted to rational polyhedra and prove that finitely generated weakly projective algebras coincide with finitely presented ones. We also prove that finite chains are the only totally ordered weakly projective examples in this variety.
Fil: Castaño, Diego Nicolás. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentina
Materia
Lukasiewicz Logic
Mv-Algebra
Implicative Algebra
Free Algebra
Projective
Finitely Presented
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:11336/64648
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/64648
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Implicative subreducts of MV-algebras: free and weakly projective objectsCastaño, Diego NicolásLukasiewicz LogicMv-AlgebraImplicative AlgebraFree AlgebraProjectiveFinitely Presentedhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this article, we explore in some detail the free and weakly projective objects of the variety of Łukasiewicz implication algebras (the implicative subreducts of MV-algebras). We review the two already known descriptions of finitely generated free algebras, giving new insights into their structure and their connection, as well as providing new proofs of the characterizations. We give a representation theorem for weakly projective algebras as algebras of certain McNaughton functions restricted to rational polyhedra and prove that finitely generated weakly projective algebras coincide with finitely presented ones. We also prove that finite chains are the only totally ordered weakly projective examples in this variety.Fil: Castaño, Diego Nicolás. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; ArgentinaBirkhauser Verlag Ag2017-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/64648Castaño, Diego Nicolás; Implicative subreducts of MV-algebras: free and weakly projective objects; Birkhauser Verlag Ag; Algebra Universalis; 78; 4; 12-2017; 579-6000002-52401420-8911CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s00012-017-0474-8info:eu-repo/semantics/altIdentifier/doi/10.1007/s00012-017-0474-8info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-10T13:05:54Zoai:ri.conicet.gov.ar:11336/64648instacron: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:34982025-09-10 13:05:54.633CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Implicative subreducts of MV-algebras: free and weakly projective objects
title Implicative subreducts of MV-algebras: free and weakly projective objects
spellingShingle Implicative subreducts of MV-algebras: free and weakly projective objects
Castaño, Diego Nicolás
Lukasiewicz Logic
Mv-Algebra
Implicative Algebra
Free Algebra
Projective
Finitely Presented
title_short Implicative subreducts of MV-algebras: free and weakly projective objects
title_full Implicative subreducts of MV-algebras: free and weakly projective objects
title_fullStr Implicative subreducts of MV-algebras: free and weakly projective objects
title_full_unstemmed Implicative subreducts of MV-algebras: free and weakly projective objects
title_sort Implicative subreducts of MV-algebras: free and weakly projective objects
dc.creator.none.fl_str_mv Castaño, Diego Nicolás
author Castaño, Diego Nicolás
author_facet Castaño, Diego Nicolás
author_role author
dc.subject.none.fl_str_mv Lukasiewicz Logic
Mv-Algebra
Implicative Algebra
Free Algebra
Projective
Finitely Presented
topic Lukasiewicz Logic
Mv-Algebra
Implicative Algebra
Free Algebra
Projective
Finitely Presented
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In this article, we explore in some detail the free and weakly projective objects of the variety of Łukasiewicz implication algebras (the implicative subreducts of MV-algebras). We review the two already known descriptions of finitely generated free algebras, giving new insights into their structure and their connection, as well as providing new proofs of the characterizations. We give a representation theorem for weakly projective algebras as algebras of certain McNaughton functions restricted to rational polyhedra and prove that finitely generated weakly projective algebras coincide with finitely presented ones. We also prove that finite chains are the only totally ordered weakly projective examples in this variety.
Fil: Castaño, Diego Nicolás. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentina
description In this article, we explore in some detail the free and weakly projective objects of the variety of Łukasiewicz implication algebras (the implicative subreducts of MV-algebras). We review the two already known descriptions of finitely generated free algebras, giving new insights into their structure and their connection, as well as providing new proofs of the characterizations. We give a representation theorem for weakly projective algebras as algebras of certain McNaughton functions restricted to rational polyhedra and prove that finitely generated weakly projective algebras coincide with finitely presented ones. We also prove that finite chains are the only totally ordered weakly projective examples in this variety.
publishDate 2017
dc.date.none.fl_str_mv 2017-12
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/11336/64648
Castaño, Diego Nicolás; Implicative subreducts of MV-algebras: free and weakly projective objects; Birkhauser Verlag Ag; Algebra Universalis; 78; 4; 12-2017; 579-600
0002-5240
1420-8911
CONICET Digital
CONICET
url http://hdl.handle.net/11336/64648
identifier_str_mv Castaño, Diego Nicolás; Implicative subreducts of MV-algebras: free and weakly projective objects; Birkhauser Verlag Ag; Algebra Universalis; 78; 4; 12-2017; 579-600
0002-5240
1420-8911
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://link.springer.com/article/10.1007/s00012-017-0474-8
info:eu-repo/semantics/altIdentifier/doi/10.1007/s00012-017-0474-8
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 Birkhauser Verlag Ag
publisher.none.fl_str_mv Birkhauser Verlag Ag
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 12.993085

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