The subvariety of commutative residuated lattices represented by twist-products

Autores
Busaniche, Manuela; Cignoli, Roberto Leonardo Oscar
Año de publicación
2014
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Given an integral commutative residuated lattice L, the product L × L can be endowed with the structure of a commutative residuated lattice with involution that we call a twist-product. In the present paper, we study the subvariety KK of commutative residuated lattices that can be represented by twist-products. We give an equational characterization of KK , a categorical interpretation of the relation among the algebraic categories of commutative integral residuated lattices and the elements in KK , and we analyze the subvariety of representable algebras in KK . Finally, we consider some specific class of bounded integral commutative residuated lattices GG , and for each fixed element L∈GL∈G , we characterize the subalgebras of the twist-product whose negative cone is L in terms of some lattice filters of L, generalizing a result by Odintsov for generalized Heyting algebras.
Fil: Busaniche, Manuela. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Matemática Aplicada "Litoral"; Argentina
Fil: Cignoli, Roberto Leonardo Oscar. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
Twist-Products
Residuated Lattices
Glivenko Residuated Lattices
Involutions
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:11336/13263
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/13263
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network_name_str CONICET Digital (CONICET)
spelling The subvariety of commutative residuated lattices represented by twist-productsBusaniche, ManuelaCignoli, Roberto Leonardo OscarTwist-ProductsResiduated LatticesGlivenko Residuated LatticesInvolutionshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Given an integral commutative residuated lattice L, the product L × L can be endowed with the structure of a commutative residuated lattice with involution that we call a twist-product. In the present paper, we study the subvariety KK of commutative residuated lattices that can be represented by twist-products. We give an equational characterization of KK , a categorical interpretation of the relation among the algebraic categories of commutative integral residuated lattices and the elements in KK , and we analyze the subvariety of representable algebras in KK . Finally, we consider some specific class of bounded integral commutative residuated lattices GG , and for each fixed element L∈GL∈G , we characterize the subalgebras of the twist-product whose negative cone is L in terms of some lattice filters of L, generalizing a result by Odintsov for generalized Heyting algebras.Fil: Busaniche, Manuela. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Matemática Aplicada "Litoral"; ArgentinaFil: Cignoli, Roberto Leonardo Oscar. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaSpringer2014-03info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/13263Busaniche, Manuela; Cignoli, Roberto Leonardo Oscar; The subvariety of commutative residuated lattices represented by twist-products; Springer; Algebra Universalis; 71; 1; 3-2014; 5-220002-5240enginfo:eu-repo/semantics/altIdentifier/doi/doi:10.1007/s00012-014-0265-4info:eu-repo/semantics/altIdentifier/url/http://link.springer.com/article/10.1007/s00012-014-0265-4info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T10:10:30Zoai:ri.conicet.gov.ar:11336/13263instacron: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 10:10:30.277CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv The subvariety of commutative residuated lattices represented by twist-products
title The subvariety of commutative residuated lattices represented by twist-products
spellingShingle The subvariety of commutative residuated lattices represented by twist-products
Busaniche, Manuela
Twist-Products
Residuated Lattices
Glivenko Residuated Lattices
Involutions
title_short The subvariety of commutative residuated lattices represented by twist-products
title_full The subvariety of commutative residuated lattices represented by twist-products
title_fullStr The subvariety of commutative residuated lattices represented by twist-products
title_full_unstemmed The subvariety of commutative residuated lattices represented by twist-products
title_sort The subvariety of commutative residuated lattices represented by twist-products
dc.creator.none.fl_str_mv Busaniche, Manuela
Cignoli, Roberto Leonardo Oscar
author Busaniche, Manuela
author_facet Busaniche, Manuela
Cignoli, Roberto Leonardo Oscar
author_role author
author2 Cignoli, Roberto Leonardo Oscar
author2_role author
dc.subject.none.fl_str_mv Twist-Products
Residuated Lattices
Glivenko Residuated Lattices
Involutions
topic Twist-Products
Residuated Lattices
Glivenko Residuated Lattices
Involutions
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Given an integral commutative residuated lattice L, the product L × L can be endowed with the structure of a commutative residuated lattice with involution that we call a twist-product. In the present paper, we study the subvariety KK of commutative residuated lattices that can be represented by twist-products. We give an equational characterization of KK , a categorical interpretation of the relation among the algebraic categories of commutative integral residuated lattices and the elements in KK , and we analyze the subvariety of representable algebras in KK . Finally, we consider some specific class of bounded integral commutative residuated lattices GG , and for each fixed element L∈GL∈G , we characterize the subalgebras of the twist-product whose negative cone is L in terms of some lattice filters of L, generalizing a result by Odintsov for generalized Heyting algebras.
Fil: Busaniche, Manuela. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Matemática Aplicada "Litoral"; Argentina
Fil: Cignoli, Roberto Leonardo Oscar. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description Given an integral commutative residuated lattice L, the product L × L can be endowed with the structure of a commutative residuated lattice with involution that we call a twist-product. In the present paper, we study the subvariety KK of commutative residuated lattices that can be represented by twist-products. We give an equational characterization of KK , a categorical interpretation of the relation among the algebraic categories of commutative integral residuated lattices and the elements in KK , and we analyze the subvariety of representable algebras in KK . Finally, we consider some specific class of bounded integral commutative residuated lattices GG , and for each fixed element L∈GL∈G , we characterize the subalgebras of the twist-product whose negative cone is L in terms of some lattice filters of L, generalizing a result by Odintsov for generalized Heyting algebras.
publishDate 2014
dc.date.none.fl_str_mv 2014-03
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/11336/13263
Busaniche, Manuela; Cignoli, Roberto Leonardo Oscar; The subvariety of commutative residuated lattices represented by twist-products; Springer; Algebra Universalis; 71; 1; 3-2014; 5-22
0002-5240
url http://hdl.handle.net/11336/13263
identifier_str_mv Busaniche, Manuela; Cignoli, Roberto Leonardo Oscar; The subvariety of commutative residuated lattices represented by twist-products; Springer; Algebra Universalis; 71; 1; 3-2014; 5-22
0002-5240
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/doi:10.1007/s00012-014-0265-4
info:eu-repo/semantics/altIdentifier/url/http://link.springer.com/article/10.1007/s00012-014-0265-4
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
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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