On implicator groupoids

Autores
Cornejo, Juan Manuel; Sankappanavar, Hanamantagouda P.
Año de publicación
2017
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In a paper published in 2012, the second author extended the well-known fact that Boolean algebras can be defined using only implication and a constant, to De Morgan algebras—this result led him to introduce, and investigate (in the same paper), the variety I of algebras, there called implication zroupoids (I-zroupoids) and here called implicator groupoids (I-groupoids), that generalize De Morgan algebras. The present paper is a continuation of the paper mentioned above and is devoted to investigating the structure of the lattice of subvarieties of I, and also to making further contributions to the theory of implicator groupoids. Several new subvarieties of I are introduced and their relationship with each other, and with the subvarieties of I which were already investigated in the paper mentioned above, are explored.
Fil: Cornejo, Juan Manuel. 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: Sankappanavar, Hanamantagouda P.. State University of New York; Estados Unidos
Materia
03g10
20n02
De Morgan Algebra
Implicator Groupoid
Primary: 06d30
Secondary: 08b15
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:11336/61084
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/61084
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling On implicator groupoidsCornejo, Juan ManuelSankappanavar, Hanamantagouda P.03g1020n02De Morgan AlgebraImplicator GroupoidPrimary: 06d30Secondary: 08b15https://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In a paper published in 2012, the second author extended the well-known fact that Boolean algebras can be defined using only implication and a constant, to De Morgan algebras—this result led him to introduce, and investigate (in the same paper), the variety I of algebras, there called implication zroupoids (I-zroupoids) and here called implicator groupoids (I-groupoids), that generalize De Morgan algebras. The present paper is a continuation of the paper mentioned above and is devoted to investigating the structure of the lattice of subvarieties of I, and also to making further contributions to the theory of implicator groupoids. Several new subvarieties of I are introduced and their relationship with each other, and with the subvarieties of I which were already investigated in the paper mentioned above, are explored.Fil: Cornejo, Juan Manuel. 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: Sankappanavar, Hanamantagouda P.. State University of New York; Estados UnidosBirkhauser Verlag Ag2017-04info: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/11336/61084Cornejo, Juan Manuel; Sankappanavar, Hanamantagouda P.; On implicator groupoids; Birkhauser Verlag Ag; Algebra Universalis; 77; 2; 4-2017; 125-1460002-5240CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://link.springer.com/content/pdf/10.1007/s00012-017-0429-0.pdfinfo:eu-repo/semantics/altIdentifier/doi/10.1007/s00012-017-0429-0info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-10T13:01:28Zoai:ri.conicet.gov.ar:11336/61084instacron: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 13:01:29.203CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv On implicator groupoids
title On implicator groupoids
spellingShingle On implicator groupoids
Cornejo, Juan Manuel
03g10
20n02
De Morgan Algebra
Implicator Groupoid
Primary: 06d30
Secondary: 08b15
title_short On implicator groupoids
title_full On implicator groupoids
title_fullStr On implicator groupoids
title_full_unstemmed On implicator groupoids
title_sort On implicator groupoids
dc.creator.none.fl_str_mv Cornejo, Juan Manuel
Sankappanavar, Hanamantagouda P.
author Cornejo, Juan Manuel
author_facet Cornejo, Juan Manuel
Sankappanavar, Hanamantagouda P.
author_role author
author2 Sankappanavar, Hanamantagouda P.
author2_role author
dc.subject.none.fl_str_mv 03g10
20n02
De Morgan Algebra
Implicator Groupoid
Primary: 06d30
Secondary: 08b15
topic 03g10
20n02
De Morgan Algebra
Implicator Groupoid
Primary: 06d30
Secondary: 08b15
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 a paper published in 2012, the second author extended the well-known fact that Boolean algebras can be defined using only implication and a constant, to De Morgan algebras—this result led him to introduce, and investigate (in the same paper), the variety I of algebras, there called implication zroupoids (I-zroupoids) and here called implicator groupoids (I-groupoids), that generalize De Morgan algebras. The present paper is a continuation of the paper mentioned above and is devoted to investigating the structure of the lattice of subvarieties of I, and also to making further contributions to the theory of implicator groupoids. Several new subvarieties of I are introduced and their relationship with each other, and with the subvarieties of I which were already investigated in the paper mentioned above, are explored.
Fil: Cornejo, Juan Manuel. 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: Sankappanavar, Hanamantagouda P.. State University of New York; Estados Unidos
description In a paper published in 2012, the second author extended the well-known fact that Boolean algebras can be defined using only implication and a constant, to De Morgan algebras—this result led him to introduce, and investigate (in the same paper), the variety I of algebras, there called implication zroupoids (I-zroupoids) and here called implicator groupoids (I-groupoids), that generalize De Morgan algebras. The present paper is a continuation of the paper mentioned above and is devoted to investigating the structure of the lattice of subvarieties of I, and also to making further contributions to the theory of implicator groupoids. Several new subvarieties of I are introduced and their relationship with each other, and with the subvarieties of I which were already investigated in the paper mentioned above, are explored.
publishDate 2017
dc.date.none.fl_str_mv 2017-04
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/11336/61084
Cornejo, Juan Manuel; Sankappanavar, Hanamantagouda P.; On implicator groupoids; Birkhauser Verlag Ag; Algebra Universalis; 77; 2; 4-2017; 125-146
0002-5240
CONICET Digital
CONICET
url http://hdl.handle.net/11336/61084
identifier_str_mv Cornejo, Juan Manuel; Sankappanavar, Hanamantagouda P.; On implicator groupoids; Birkhauser Verlag Ag; Algebra Universalis; 77; 2; 4-2017; 125-146
0002-5240
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/content/pdf/10.1007/s00012-017-0429-0.pdf
info:eu-repo/semantics/altIdentifier/doi/10.1007/s00012-017-0429-0
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/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
_version_ 1842979952044015616
score 12.993085

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