Monadic MV-algebras I: a study of subvarieties

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 and classify some important subvarieties of the variety of monadic MV-algebras. We introduce the notion of width of a monadic MV-algebra and we prove that the equational class of monadic MV-algebras of finite width k is generated by the monadic MV-algebra [0, 1] k. We describe completely the lattice of subvarieties of the subvariety V([0, 1] k) generated by [0, 1] k. We prove that the subvariety generated by a subdirectly irreducible monadic MV-algebra of finite width depends on the order and rank of ∀A, the partition associated to A of the set of coatoms of the boolean subalgebra B(A) of its complemented elements, and the width of the algebra. We also give an equational basis for each proper subvariety in V([0, 1] k). Finally, we give some results about subvarieties of infinite width.
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
Functional Representation
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:11336/29824
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Monadic MV-algebras I: a study of subvarietiesCimadamore, Cecilia RossanaDíaz Varela, José PatricioMonadic Mv-AlgebrasFunctional RepresentationSubvarietiesEquational Baseshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper, we study and classify some important subvarieties of the variety of monadic MV-algebras. We introduce the notion of width of a monadic MV-algebra and we prove that the equational class of monadic MV-algebras of finite width k is generated by the monadic MV-algebra [0, 1] k. We describe completely the lattice of subvarieties of the subvariety V([0, 1] k) generated by [0, 1] k. We prove that the subvariety generated by a subdirectly irreducible monadic MV-algebra of finite width depends on the order and rank of ∀A, the partition associated to A of the set of coatoms of the boolean subalgebra B(A) of its complemented elements, and the width of the algebra. We also give an equational basis for each proper subvariety in V([0, 1] k). Finally, we give some results about subvarieties of infinite width.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; ArgentinaSpringer2014-01info: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/11336/29824Cimadamore, Cecilia Rossana; Díaz Varela, José Patricio; Monadic MV-algebras I: a study of subvarieties; Springer; Algebra Universalis; 71; 1; 1-2014; 71-1000002-52401420-8911CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1007/s00012-014-0266-3info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs00012-014-0266-3info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:59:10Zoai:ri.conicet.gov.ar:11336/29824instacron: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 09:59:11.276CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Monadic MV-algebras I: a study of subvarieties
title Monadic MV-algebras I: a study of subvarieties
spellingShingle Monadic MV-algebras I: a study of subvarieties
Cimadamore, Cecilia Rossana
Monadic Mv-Algebras
Functional Representation
Subvarieties
Equational Bases
title_short Monadic MV-algebras I: a study of subvarieties
title_full Monadic MV-algebras I: a study of subvarieties
title_fullStr Monadic MV-algebras I: a study of subvarieties
title_full_unstemmed Monadic MV-algebras I: a study of subvarieties
title_sort Monadic MV-algebras I: a study of subvarieties
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
Functional Representation
Subvarieties
Equational Bases
topic Monadic Mv-Algebras
Functional Representation
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 and classify some important subvarieties of the variety of monadic MV-algebras. We introduce the notion of width of a monadic MV-algebra and we prove that the equational class of monadic MV-algebras of finite width k is generated by the monadic MV-algebra [0, 1] k. We describe completely the lattice of subvarieties of the subvariety V([0, 1] k) generated by [0, 1] k. We prove that the subvariety generated by a subdirectly irreducible monadic MV-algebra of finite width depends on the order and rank of ∀A, the partition associated to A of the set of coatoms of the boolean subalgebra B(A) of its complemented elements, and the width of the algebra. We also give an equational basis for each proper subvariety in V([0, 1] k). Finally, we give some results about subvarieties of infinite width.
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 and classify some important subvarieties of the variety of monadic MV-algebras. We introduce the notion of width of a monadic MV-algebra and we prove that the equational class of monadic MV-algebras of finite width k is generated by the monadic MV-algebra [0, 1] k. We describe completely the lattice of subvarieties of the subvariety V([0, 1] k) generated by [0, 1] k. We prove that the subvariety generated by a subdirectly irreducible monadic MV-algebra of finite width depends on the order and rank of ∀A, the partition associated to A of the set of coatoms of the boolean subalgebra B(A) of its complemented elements, and the width of the algebra. We also give an equational basis for each proper subvariety in V([0, 1] k). Finally, we give some results about subvarieties of infinite width.
publishDate 2014
dc.date.none.fl_str_mv 2014-01
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/11336/29824
Cimadamore, Cecilia Rossana; Díaz Varela, José Patricio; Monadic MV-algebras I: a study of subvarieties; Springer; Algebra Universalis; 71; 1; 1-2014; 71-100
0002-5240
1420-8911
CONICET Digital
CONICET
url http://hdl.handle.net/11336/29824
identifier_str_mv Cimadamore, Cecilia Rossana; Díaz Varela, José Patricio; Monadic MV-algebras I: a study of subvarieties; Springer; Algebra Universalis; 71; 1; 1-2014; 71-100
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/s00012-014-0266-3
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs00012-014-0266-3
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 13.13397

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