Monadic MV-algebras II: Monadic implicational subreducts

Autores
Cimadamore, Cecilia Rossana; Díaz Varela, José Patricio
Año de publicación
2014
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper, we study the class of all monadic implicational subreducts, that is, the {→, ∀, 1}-subreducts of the class of monadic MV-algebras. We prove that this class is an equational class, which we denote by ML, and we give an equational basis for this variety. An algebra in ML is called a monadic Lukasiewicz implication algebra. We characterize the subdirectly irreducible members of ML and the congruences of every monadic Lukasiewicz implication algebra by monadic filters. We prove that ML is generated by its finite members. Finally, we completely describe the lattice of subvarieties, and we give an equational basis for each proper subvariety.
Fil: Cimadamore, Cecilia Rossana. 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
Fil: Díaz Varela, José Patricio. 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
Monadic Mv-Algebras
Monadic Implicationa Subreducts
Lukasiewicz Implication Algebras
Subvarieties
Equational Bases
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:11336/29828
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/29828
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Monadic MV-algebras II: Monadic implicational subreductsCimadamore, Cecilia RossanaDíaz Varela, José PatricioMonadic Mv-AlgebrasMonadic Implicationa SubreductsLukasiewicz Implication AlgebrasSubvarietiesEquational Baseshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper, we study the class of all monadic implicational subreducts, that is, the {→, ∀, 1}-subreducts of the class of monadic MV-algebras. We prove that this class is an equational class, which we denote by ML, and we give an equational basis for this variety. An algebra in ML is called a monadic Lukasiewicz implication algebra. We characterize the subdirectly irreducible members of ML and the congruences of every monadic Lukasiewicz implication algebra by monadic filters. We prove that ML is generated by its finite members. Finally, we completely describe the lattice of subvarieties, and we give an equational basis for each proper subvariety.Fil: Cimadamore, Cecilia Rossana. 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; ArgentinaFil: Díaz Varela, José Patricio. 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; ArgentinaSpringer2014-03info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/29828Cimadamore, Cecilia Rossana; Díaz Varela, José Patricio; Monadic MV-algebras II: Monadic implicational subreducts; Springer; Algebra Universalis; 71; 3; 3-2014; 201-2190002-52401420-8911CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1007/s00012-014-0277-0info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs00012-014-0277-0info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T14:47:01Zoai:ri.conicet.gov.ar:11336/29828instacron: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:34982025-10-15 14:47:02.102CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Monadic MV-algebras II: Monadic implicational subreducts
title Monadic MV-algebras II: Monadic implicational subreducts
spellingShingle Monadic MV-algebras II: Monadic implicational subreducts
Cimadamore, Cecilia Rossana
Monadic Mv-Algebras
Monadic Implicationa Subreducts
Lukasiewicz Implication Algebras
Subvarieties
Equational Bases
title_short Monadic MV-algebras II: Monadic implicational subreducts
title_full Monadic MV-algebras II: Monadic implicational subreducts
title_fullStr Monadic MV-algebras II: Monadic implicational subreducts
title_full_unstemmed Monadic MV-algebras II: Monadic implicational subreducts
title_sort Monadic MV-algebras II: Monadic implicational subreducts
dc.creator.none.fl_str_mv Cimadamore, Cecilia Rossana
Díaz Varela, José Patricio
author Cimadamore, Cecilia Rossana
author_facet Cimadamore, Cecilia Rossana
Díaz Varela, José Patricio
author_role author
author2 Díaz Varela, José Patricio
author2_role author
dc.subject.none.fl_str_mv Monadic Mv-Algebras
Monadic Implicationa Subreducts
Lukasiewicz Implication Algebras
Subvarieties
Equational Bases
topic Monadic Mv-Algebras
Monadic Implicationa Subreducts
Lukasiewicz Implication Algebras
Subvarieties
Equational Bases
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 paper, we study the class of all monadic implicational subreducts, that is, the {→, ∀, 1}-subreducts of the class of monadic MV-algebras. We prove that this class is an equational class, which we denote by ML, and we give an equational basis for this variety. An algebra in ML is called a monadic Lukasiewicz implication algebra. We characterize the subdirectly irreducible members of ML and the congruences of every monadic Lukasiewicz implication algebra by monadic filters. We prove that ML is generated by its finite members. Finally, we completely describe the lattice of subvarieties, and we give an equational basis for each proper subvariety.
Fil: Cimadamore, Cecilia Rossana. 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
Fil: Díaz Varela, José Patricio. 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 paper, we study the class of all monadic implicational subreducts, that is, the {→, ∀, 1}-subreducts of the class of monadic MV-algebras. We prove that this class is an equational class, which we denote by ML, and we give an equational basis for this variety. An algebra in ML is called a monadic Lukasiewicz implication algebra. We characterize the subdirectly irreducible members of ML and the congruences of every monadic Lukasiewicz implication algebra by monadic filters. We prove that ML is generated by its finite members. Finally, we completely describe the lattice of subvarieties, and we give an equational basis for each proper subvariety.
publishDate 2014
dc.date.none.fl_str_mv 2014-03
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/11336/29828
Cimadamore, Cecilia Rossana; Díaz Varela, José Patricio; Monadic MV-algebras II: Monadic implicational subreducts; Springer; Algebra Universalis; 71; 3; 3-2014; 201-219
0002-5240
1420-8911
CONICET Digital
CONICET
url http://hdl.handle.net/11336/29828
identifier_str_mv Cimadamore, Cecilia Rossana; Díaz Varela, José Patricio; Monadic MV-algebras II: Monadic implicational subreducts; Springer; Algebra Universalis; 71; 3; 3-2014; 201-219
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/doi/10.1007/s00012-014-0277-0
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs00012-014-0277-0
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
application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
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 13.22299

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