On a Definition of a Variety of Monadic ℓ-Groups

Autores
Castiglioni, José Luis; Lewin, Renato A.; Sagastume, Marta Susana
Año de publicación
2013
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper we expand previous results obtained in [2] about the study of categorical equivalence between the category IRL 0 of integral residuated lattices with bottom, which generalize MV-algebras and a category whose objects are called c-differential residuated lattices. The equivalence is given by a functor K∙, motivated by an old construction due to J. Kalman, which was studied by Cignoli in [3] in the context of Heyting and Nelson algebras. These results are then specialized to the case of MV-algebras and the corresponding category MV∙ of monadic MV-algebras induced by “Kalman’s functor” K∙. Moreover, we extend the construction to ℓ-groups introducing the new category of monadic ℓ-groups together with a functor Γ♯, that is “parallel” to the well known functor Γ between ℓ and MV-algebras.
Facultad de Ciencias Exactas
Materia
Ciencias Exactas
Matemática
Monadic ℓ-groups
Monadic MV algebras
Residuated Lattices
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by/4.0/
Repositorio
SEDICI (UNLP)
Institución
Universidad Nacional de La Plata
OAI Identificador
oai:sedici.unlp.edu.ar:10915/139814
Acceder
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oai_identifier_str oai:sedici.unlp.edu.ar:10915/139814
network_acronym_str SEDICI
repository_id_str 1329
network_name_str SEDICI (UNLP)
spelling On a Definition of a Variety of Monadic ℓ-GroupsCastiglioni, José LuisLewin, Renato A.Sagastume, Marta SusanaCiencias ExactasMatemáticaMonadic ℓ-groupsMonadic MV algebrasResiduated LatticesIn this paper we expand previous results obtained in [2] about the study of categorical equivalence between the category IRL 0 of integral residuated lattices with bottom, which generalize MV-algebras and a category whose objects are called c-differential residuated lattices. The equivalence is given by a functor K∙, motivated by an old construction due to J. Kalman, which was studied by Cignoli in [3] in the context of Heyting and Nelson algebras. These results are then specialized to the case of MV-algebras and the corresponding category MV∙ of monadic MV-algebras induced by “Kalman’s functor” K∙. Moreover, we extend the construction to ℓ-groups introducing the new category of monadic ℓ-groups together with a functor Γ♯, that is “parallel” to the well known functor Γ between ℓ and MV-algebras.Facultad de Ciencias Exactas2013-02-27info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdf67-92http://sedici.unlp.edu.ar/handle/10915/139814enginfo:eu-repo/semantics/altIdentifier/issn/0039-3215info:eu-repo/semantics/altIdentifier/issn/1572-8730info:eu-repo/semantics/altIdentifier/doi/10.1007/s11225-012-9464-1info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/4.0/Creative Commons Attribution 4.0 International (CC BY 4.0)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2025-10-15T11:23:53Zoai:sedici.unlp.edu.ar:10915/139814Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-10-15 11:23:54.168SEDICI (UNLP) - Universidad Nacional de La Platafalse
dc.title.none.fl_str_mv On a Definition of a Variety of Monadic ℓ-Groups
title On a Definition of a Variety of Monadic ℓ-Groups
spellingShingle On a Definition of a Variety of Monadic ℓ-Groups
Castiglioni, José Luis
Ciencias Exactas
Matemática
Monadic ℓ-groups
Monadic MV algebras
Residuated Lattices
title_short On a Definition of a Variety of Monadic ℓ-Groups
title_full On a Definition of a Variety of Monadic ℓ-Groups
title_fullStr On a Definition of a Variety of Monadic ℓ-Groups
title_full_unstemmed On a Definition of a Variety of Monadic ℓ-Groups
title_sort On a Definition of a Variety of Monadic ℓ-Groups
dc.creator.none.fl_str_mv Castiglioni, José Luis
Lewin, Renato A.
Sagastume, Marta Susana
author Castiglioni, José Luis
author_facet Castiglioni, José Luis
Lewin, Renato A.
Sagastume, Marta Susana
author_role author
author2 Lewin, Renato A.
Sagastume, Marta Susana
author2_role author
author
dc.subject.none.fl_str_mv Ciencias Exactas
Matemática
Monadic ℓ-groups
Monadic MV algebras
Residuated Lattices
topic Ciencias Exactas
Matemática
Monadic ℓ-groups
Monadic MV algebras
Residuated Lattices
dc.description.none.fl_txt_mv In this paper we expand previous results obtained in [2] about the study of categorical equivalence between the category IRL 0 of integral residuated lattices with bottom, which generalize MV-algebras and a category whose objects are called c-differential residuated lattices. The equivalence is given by a functor K∙, motivated by an old construction due to J. Kalman, which was studied by Cignoli in [3] in the context of Heyting and Nelson algebras. These results are then specialized to the case of MV-algebras and the corresponding category MV∙ of monadic MV-algebras induced by “Kalman’s functor” K∙. Moreover, we extend the construction to ℓ-groups introducing the new category of monadic ℓ-groups together with a functor Γ♯, that is “parallel” to the well known functor Γ between ℓ and MV-algebras.
Facultad de Ciencias Exactas
description In this paper we expand previous results obtained in [2] about the study of categorical equivalence between the category IRL 0 of integral residuated lattices with bottom, which generalize MV-algebras and a category whose objects are called c-differential residuated lattices. The equivalence is given by a functor K∙, motivated by an old construction due to J. Kalman, which was studied by Cignoli in [3] in the context of Heyting and Nelson algebras. These results are then specialized to the case of MV-algebras and the corresponding category MV∙ of monadic MV-algebras induced by “Kalman’s functor” K∙. Moreover, we extend the construction to ℓ-groups introducing the new category of monadic ℓ-groups together with a functor Γ♯, that is “parallel” to the well known functor Γ between ℓ and MV-algebras.
publishDate 2013
dc.date.none.fl_str_mv 2013-02-27
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
Articulo
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://sedici.unlp.edu.ar/handle/10915/139814
url http://sedici.unlp.edu.ar/handle/10915/139814
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/issn/0039-3215
info:eu-repo/semantics/altIdentifier/issn/1572-8730
info:eu-repo/semantics/altIdentifier/doi/10.1007/s11225-012-9464-1
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by/4.0/
Creative Commons Attribution 4.0 International (CC BY 4.0)
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by/4.0/
Creative Commons Attribution 4.0 International (CC BY 4.0)
dc.format.none.fl_str_mv application/pdf
67-92
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instname:Universidad Nacional de La Plata
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reponame_str SEDICI (UNLP)
collection SEDICI (UNLP)
instname_str Universidad Nacional de La Plata
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institution UNLP
repository.name.fl_str_mv SEDICI (UNLP) - Universidad Nacional de La Plata
repository.mail.fl_str_mv alira@sedici.unlp.edu.ar
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