Factor congruences in BCK-algebras

In this paper, we characterize factor congruences in the quasivariety of BCK-algebras. As an application we prove that the free algebra over an infinite set of generators is indecomposable in any subvariety of BCK-algebras. We also study the decomposability of free algebras in the variety of hoop re...

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Detalles Bibliográficos
Autores: Abad, Manuel, Díaz Varela, José Patricio
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2008
País:Argentina
Institución:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/79644
Acceso en línea:http://hdl.handle.net/11336/79644
Access Level:acceso abierto
Palabra clave:Bck-Algebras
Decomposability
Factor Congruences
Free Algebras
Hoops
Implicative Filters
Pocrims
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
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spelling Factor congruences in BCK-algebrasAbad, ManuelDíaz Varela, José PatricioBck-AlgebrasDecomposabilityFactor CongruencesFree AlgebrasHoopsImplicative FiltersPocrimshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper, we characterize factor congruences in the quasivariety of BCK-algebras. As an application we prove that the free algebra over an infinite set of generators is indecomposable in any subvariety of BCK-algebras. We also study the decomposability of free algebras in the variety of hoop residuation algebras (HBCK) and its subvarieties. We prove that free algebras in a non k-potent subvariety of HBCK are indecomposable while finitely generated free algebras in k-potent subvarieties have a unique non-trivial decomposition into a direct product of two factors, and one of them is the two-element implication algebra.Fil: Abad, Manuel. Universidad Nacional del Sur. Departamento de Matemática; 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; ArgentinaSpringer Verlag Berlín2008-07-29info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/79644Abad, Manuel; Díaz Varela, José Patricio; Factor congruences in BCK-algebras; Springer Verlag Berlín; Soft Computing; 13; 10; 29-7-2008; 1007-10121432-76431433-7479CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s00500-008-0346-4info:eu-repo/semantics/altIdentifier/doi/10.1007/s00500-008-0346-4info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2024-05-08T13:50:28Zoai:ri.conicet.gov.ar:11336/79644instacron: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:34982024-05-08 13:50:28.936CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Factor congruences in BCK-algebras
title Factor congruences in BCK-algebras
spellingShingle Factor congruences in BCK-algebras
Abad, Manuel
Bck-Algebras
Decomposability
Factor Congruences
Free Algebras
Hoops
Implicative Filters
Pocrims
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
title_short Factor congruences in BCK-algebras
title_full Factor congruences in BCK-algebras
title_fullStr Factor congruences in BCK-algebras
title_full_unstemmed Factor congruences in BCK-algebras
title_sort Factor congruences in BCK-algebras
dc.creator.none.fl_str_mv Abad, Manuel
Díaz Varela, José Patricio
author Abad, Manuel
author_facet Abad, Manuel
Díaz Varela, José Patricio
author_role author
author2 Díaz Varela, José Patricio
author2_role author
dc.subject.none.fl_str_mv Bck-Algebras
Decomposability
Factor Congruences
Free Algebras
Hoops
Implicative Filters
Pocrims
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
topic Bck-Algebras
Decomposability
Factor Congruences
Free Algebras
Hoops
Implicative Filters
Pocrims
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
description In this paper, we characterize factor congruences in the quasivariety of BCK-algebras. As an application we prove that the free algebra over an infinite set of generators is indecomposable in any subvariety of BCK-algebras. We also study the decomposability of free algebras in the variety of hoop residuation algebras (HBCK) and its subvarieties. We prove that free algebras in a non k-potent subvariety of HBCK are indecomposable while finitely generated free algebras in k-potent subvarieties have a unique non-trivial decomposition into a direct product of two factors, and one of them is the two-element implication algebra.
publishDate 2008
dc.date.none.fl_str_mv 2008-07-29
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/11336/79644
Abad, Manuel; Díaz Varela, José Patricio; Factor congruences in BCK-algebras; Springer Verlag Berlín; Soft Computing; 13; 10; 29-7-2008; 1007-1012
1432-7643
1433-7479
CONICET Digital
CONICET
url http://hdl.handle.net/11336/79644
identifier_str_mv Abad, Manuel; Díaz Varela, José Patricio; Factor congruences in BCK-algebras; Springer Verlag Berlín; Soft Computing; 13; 10; 29-7-2008; 1007-1012
1432-7643
1433-7479
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/s00500-008-0346-4
info:eu-repo/semantics/altIdentifier/doi/10.1007/s00500-008-0346-4
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 Springer Verlag Berlín
publisher.none.fl_str_mv Springer Verlag Berlín
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
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 15.812429

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