Frontal operators in distributive lattices with a generalized implication

Autores
Celani, Sergio Arturo; San Martín, Hernán Javier
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We introduce a family of extensions of bounded distributive lattices. These extensions are obtained by adding two operations: an internal unary operation, and a function (called generalized implication) that maps pair of elements to ideals of the lattice. A bounded distributive lattice with a generalized implication is called gi-lattice in [4]. The main goal of this paper is to introduce and study the category of frontal gi-lattices (and some subcategories of it). This category can be seen as a generalization of the category of frontal weak Heyting algebras ([9]). In particular, we study the case of frontal gi-lattices where the generalized implication is defined as the annihilator ([11], [15]). We give a Priestley’s style duality for each one of the new classes of structures considered.
Fil: Celani, Sergio Arturo. Universidad Nacional del Centro de la Provincia de Buenos Aires.Facultad de Ciencias Exactas; Argentina
Fil: San Martín, Hernán Javier. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
Distributive Lattices
Generalized Implication
Frontal Operators
Priestley Duality
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:11336/45974
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/45974
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Frontal operators in distributive lattices with a generalized implicationCelani, Sergio ArturoSan Martín, Hernán JavierDistributive LatticesGeneralized ImplicationFrontal OperatorsPriestley Dualityhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We introduce a family of extensions of bounded distributive lattices. These extensions are obtained by adding two operations: an internal unary operation, and a function (called generalized implication) that maps pair of elements to ideals of the lattice. A bounded distributive lattice with a generalized implication is called gi-lattice in [4]. The main goal of this paper is to introduce and study the category of frontal gi-lattices (and some subcategories of it). This category can be seen as a generalization of the category of frontal weak Heyting algebras ([9]). In particular, we study the case of frontal gi-lattices where the generalized implication is defined as the annihilator ([11], [15]). We give a Priestley’s style duality for each one of the new classes of structures considered.Fil: Celani, Sergio Arturo. Universidad Nacional del Centro de la Provincia de Buenos Aires.Facultad de Ciencias Exactas; ArgentinaFil: San Martín, Hernán Javier. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaWorldScientific Open Access2015-09info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/45974Celani, Sergio Arturo; San Martín, Hernán Javier; Frontal operators in distributive lattices with a generalized implication; WorldScientific Open Access; Asian-European Journal of Mathematics; 8; 3; 9-2015; 1-221793-7183CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1142/S1793557115500394info:eu-repo/semantics/altIdentifier/url/https://www.worldscientific.com/doi/abs/10.1142/S1793557115500394info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:45:31Zoai:ri.conicet.gov.ar:11336/45974instacron: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 09:45:31.666CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Frontal operators in distributive lattices with a generalized implication
title Frontal operators in distributive lattices with a generalized implication
spellingShingle Frontal operators in distributive lattices with a generalized implication
Celani, Sergio Arturo
Distributive Lattices
Generalized Implication
Frontal Operators
Priestley Duality
title_short Frontal operators in distributive lattices with a generalized implication
title_full Frontal operators in distributive lattices with a generalized implication
title_fullStr Frontal operators in distributive lattices with a generalized implication
title_full_unstemmed Frontal operators in distributive lattices with a generalized implication
title_sort Frontal operators in distributive lattices with a generalized implication
dc.creator.none.fl_str_mv Celani, Sergio Arturo
San Martín, Hernán Javier
author Celani, Sergio Arturo
author_facet Celani, Sergio Arturo
San Martín, Hernán Javier
author_role author
author2 San Martín, Hernán Javier
author2_role author
dc.subject.none.fl_str_mv Distributive Lattices
Generalized Implication
Frontal Operators
Priestley Duality
topic Distributive Lattices
Generalized Implication
Frontal Operators
Priestley Duality
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We introduce a family of extensions of bounded distributive lattices. These extensions are obtained by adding two operations: an internal unary operation, and a function (called generalized implication) that maps pair of elements to ideals of the lattice. A bounded distributive lattice with a generalized implication is called gi-lattice in [4]. The main goal of this paper is to introduce and study the category of frontal gi-lattices (and some subcategories of it). This category can be seen as a generalization of the category of frontal weak Heyting algebras ([9]). In particular, we study the case of frontal gi-lattices where the generalized implication is defined as the annihilator ([11], [15]). We give a Priestley’s style duality for each one of the new classes of structures considered.
Fil: Celani, Sergio Arturo. Universidad Nacional del Centro de la Provincia de Buenos Aires.Facultad de Ciencias Exactas; Argentina
Fil: San Martín, Hernán Javier. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description We introduce a family of extensions of bounded distributive lattices. These extensions are obtained by adding two operations: an internal unary operation, and a function (called generalized implication) that maps pair of elements to ideals of the lattice. A bounded distributive lattice with a generalized implication is called gi-lattice in [4]. The main goal of this paper is to introduce and study the category of frontal gi-lattices (and some subcategories of it). This category can be seen as a generalization of the category of frontal weak Heyting algebras ([9]). In particular, we study the case of frontal gi-lattices where the generalized implication is defined as the annihilator ([11], [15]). We give a Priestley’s style duality for each one of the new classes of structures considered.
publishDate 2015
dc.date.none.fl_str_mv 2015-09
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/11336/45974
Celani, Sergio Arturo; San Martín, Hernán Javier; Frontal operators in distributive lattices with a generalized implication; WorldScientific Open Access; Asian-European Journal of Mathematics; 8; 3; 9-2015; 1-22
1793-7183
CONICET Digital
CONICET
url http://hdl.handle.net/11336/45974
identifier_str_mv Celani, Sergio Arturo; San Martín, Hernán Javier; Frontal operators in distributive lattices with a generalized implication; WorldScientific Open Access; Asian-European Journal of Mathematics; 8; 3; 9-2015; 1-22
1793-7183
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1142/S1793557115500394
info:eu-repo/semantics/altIdentifier/url/https://www.worldscientific.com/doi/abs/10.1142/S1793557115500394
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 WorldScientific Open Access
publisher.none.fl_str_mv WorldScientific Open Access
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_ 1842268736417955840
score 13.13397

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