Implicit definition of the quaternary discriminator

Autores
Campercholi, Miguel Alejandro Carlos; Vaggione, Diego Jose
Año de publicación
2012
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Let A be an algebra. A function f: A n → A is implicitly definable by a system of term equations Λ t i(x i,...,x n,z)if f is the only n-ary operation on A making the identities t i(x,f(x))≈ s i(x,f(x)) hold in A. Let K be a class of non-trivial algebras. We prove that the quaternary discriminator is implicitly definable on every member of K (via the same system) iff K is contained in the class of relatively simple members of some relatively semisimple quasivariety with equationally definable relative principal congruences. As an application, we obtain a characterization of the relatively permutable members of such type of quasivarieties. Furthermore, we prove that every algebra in such a quasivariety has a unique relatively permutable extension. © 2012 Springer Basel AG.
Fil: Campercholi, Miguel Alejandro Carlos. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomia y Física. Sección Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina
Fil: Vaggione, Diego Jose. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomia y Física. Sección Matemática; Argentina
Materia
EQUATIONALLY DEFINABLE PRINCIPAL CONGRUENCES
IMPLICIT EQUATIONAL DEFINITION
QUATERNARY DISCRIMINATOR
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:11336/198846
Acceder
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repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Implicit definition of the quaternary discriminatorCampercholi, Miguel Alejandro CarlosVaggione, Diego JoseEQUATIONALLY DEFINABLE PRINCIPAL CONGRUENCESIMPLICIT EQUATIONAL DEFINITIONQUATERNARY DISCRIMINATORhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Let A be an algebra. A function f: A n → A is implicitly definable by a system of term equations Λ t i(x i,...,x n,z)if f is the only n-ary operation on A making the identities t i(x,f(x))≈ s i(x,f(x)) hold in A. Let K be a class of non-trivial algebras. We prove that the quaternary discriminator is implicitly definable on every member of K (via the same system) iff K is contained in the class of relatively simple members of some relatively semisimple quasivariety with equationally definable relative principal congruences. As an application, we obtain a characterization of the relatively permutable members of such type of quasivarieties. Furthermore, we prove that every algebra in such a quasivariety has a unique relatively permutable extension. © 2012 Springer Basel AG.Fil: Campercholi, Miguel Alejandro Carlos. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomia y Física. Sección Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; ArgentinaFil: Vaggione, Diego Jose. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomia y Física. Sección Matemática; ArgentinaBirkhauser Verlag Ag2012-10info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/zipapplication/pdfhttp://hdl.handle.net/11336/198846Campercholi, Miguel Alejandro Carlos; Vaggione, Diego Jose; Implicit definition of the quaternary discriminator; Birkhauser Verlag Ag; Algebra Universalis; 68; 1-2; 10-2012; 1-160002-52401420-8911CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s00012-012-0189-9info:eu-repo/semantics/altIdentifier/doi/10.1007/s00012-012-0189-9info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-10T13:14:07Zoai:ri.conicet.gov.ar:11336/198846instacron: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 13:14:08.228CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Implicit definition of the quaternary discriminator
title Implicit definition of the quaternary discriminator
spellingShingle Implicit definition of the quaternary discriminator
Campercholi, Miguel Alejandro Carlos
EQUATIONALLY DEFINABLE PRINCIPAL CONGRUENCES
IMPLICIT EQUATIONAL DEFINITION
QUATERNARY DISCRIMINATOR
title_short Implicit definition of the quaternary discriminator
title_full Implicit definition of the quaternary discriminator
title_fullStr Implicit definition of the quaternary discriminator
title_full_unstemmed Implicit definition of the quaternary discriminator
title_sort Implicit definition of the quaternary discriminator
dc.creator.none.fl_str_mv Campercholi, Miguel Alejandro Carlos
Vaggione, Diego Jose
author Campercholi, Miguel Alejandro Carlos
author_facet Campercholi, Miguel Alejandro Carlos
Vaggione, Diego Jose
author_role author
author2 Vaggione, Diego Jose
author2_role author
dc.subject.none.fl_str_mv EQUATIONALLY DEFINABLE PRINCIPAL CONGRUENCES
IMPLICIT EQUATIONAL DEFINITION
QUATERNARY DISCRIMINATOR
topic EQUATIONALLY DEFINABLE PRINCIPAL CONGRUENCES
IMPLICIT EQUATIONAL DEFINITION
QUATERNARY DISCRIMINATOR
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Let A be an algebra. A function f: A n → A is implicitly definable by a system of term equations Λ t i(x i,...,x n,z)if f is the only n-ary operation on A making the identities t i(x,f(x))≈ s i(x,f(x)) hold in A. Let K be a class of non-trivial algebras. We prove that the quaternary discriminator is implicitly definable on every member of K (via the same system) iff K is contained in the class of relatively simple members of some relatively semisimple quasivariety with equationally definable relative principal congruences. As an application, we obtain a characterization of the relatively permutable members of such type of quasivarieties. Furthermore, we prove that every algebra in such a quasivariety has a unique relatively permutable extension. © 2012 Springer Basel AG.
Fil: Campercholi, Miguel Alejandro Carlos. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomia y Física. Sección Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina
Fil: Vaggione, Diego Jose. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomia y Física. Sección Matemática; Argentina
description Let A be an algebra. A function f: A n → A is implicitly definable by a system of term equations Λ t i(x i,...,x n,z)if f is the only n-ary operation on A making the identities t i(x,f(x))≈ s i(x,f(x)) hold in A. Let K be a class of non-trivial algebras. We prove that the quaternary discriminator is implicitly definable on every member of K (via the same system) iff K is contained in the class of relatively simple members of some relatively semisimple quasivariety with equationally definable relative principal congruences. As an application, we obtain a characterization of the relatively permutable members of such type of quasivarieties. Furthermore, we prove that every algebra in such a quasivariety has a unique relatively permutable extension. © 2012 Springer Basel AG.
publishDate 2012
dc.date.none.fl_str_mv 2012-10
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/11336/198846
Campercholi, Miguel Alejandro Carlos; Vaggione, Diego Jose; Implicit definition of the quaternary discriminator; Birkhauser Verlag Ag; Algebra Universalis; 68; 1-2; 10-2012; 1-16
0002-5240
1420-8911
CONICET Digital
CONICET
url http://hdl.handle.net/11336/198846
identifier_str_mv Campercholi, Miguel Alejandro Carlos; Vaggione, Diego Jose; Implicit definition of the quaternary discriminator; Birkhauser Verlag Ag; Algebra Universalis; 68; 1-2; 10-2012; 1-16
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/s00012-012-0189-9
info:eu-repo/semantics/altIdentifier/doi/10.1007/s00012-012-0189-9
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/zip
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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