Remarks on annihilators preserving congruence relations

Autores
Celani, Sergio Arturo
Año de publicación
2012
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this note we shall give some results on annihilators preserving congruence relations, or AP-congruences, in bounded distributive lattices. We shall give some new characterizations, and a topological interpretation of the notion of annihilator preserving congruences introduced in [JANOWITZ, M. F.: Annihilator preserving congruence relations of lattices, Algebra Universalis 5 (1975), 391–394]. As an application of these results, we shall prove that the quotient of a quasicomplemented lattice by means of a AP-congruence is a quasicomplemented lattice. Similarly, we will prove that the quotient of a normal latttice by means of a AP-congruence is also a normal lattice.
Fil: Celani, Sergio Arturo. Universidad Nacional del Centro de la Provincia de Buenos Aires. Facultad de Ciencias Exactas. Núcleo Consolidado de Matemática Pura y Aplicada; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Tandil; Argentina
Materia
ANNIHILATOR
CONGRUENCES
NORMAL LATTICES
PRIESTLEY SPACES
QUASICOMPLEMENTED LATTICES
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:11336/208810
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/208810
network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling Remarks on annihilators preserving congruence relationsCelani, Sergio ArturoANNIHILATORCONGRUENCESNORMAL LATTICESPRIESTLEY SPACESQUASICOMPLEMENTED LATTICEShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this note we shall give some results on annihilators preserving congruence relations, or AP-congruences, in bounded distributive lattices. We shall give some new characterizations, and a topological interpretation of the notion of annihilator preserving congruences introduced in [JANOWITZ, M. F.: Annihilator preserving congruence relations of lattices, Algebra Universalis 5 (1975), 391–394]. As an application of these results, we shall prove that the quotient of a quasicomplemented lattice by means of a AP-congruence is a quasicomplemented lattice. Similarly, we will prove that the quotient of a normal latttice by means of a AP-congruence is also a normal lattice.Fil: Celani, Sergio Arturo. Universidad Nacional del Centro de la Provincia de Buenos Aires. Facultad de Ciencias Exactas. Núcleo Consolidado de Matemática Pura y Aplicada; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Tandil; ArgentinaVersita2012-05info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/208810Celani, Sergio Arturo; Remarks on annihilators preserving congruence relations; Versita; Mathematica Slovaca; 62; 3; 5-2012; 389-3980139-9918CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.2478/s12175-012-0016-yinfo:eu-repo/semantics/altIdentifier/doi/10.2478/s12175-012-0016-yinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:55:24Zoai:ri.conicet.gov.ar:11336/208810instacron: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 09:55:25.343CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Remarks on annihilators preserving congruence relations
title Remarks on annihilators preserving congruence relations
spellingShingle Remarks on annihilators preserving congruence relations
Celani, Sergio Arturo
ANNIHILATOR
CONGRUENCES
NORMAL LATTICES
PRIESTLEY SPACES
QUASICOMPLEMENTED LATTICES
title_short Remarks on annihilators preserving congruence relations
title_full Remarks on annihilators preserving congruence relations
title_fullStr Remarks on annihilators preserving congruence relations
title_full_unstemmed Remarks on annihilators preserving congruence relations
title_sort Remarks on annihilators preserving congruence relations
dc.creator.none.fl_str_mv Celani, Sergio Arturo
author Celani, Sergio Arturo
author_facet Celani, Sergio Arturo
author_role author
dc.subject.none.fl_str_mv ANNIHILATOR
CONGRUENCES
NORMAL LATTICES
PRIESTLEY SPACES
QUASICOMPLEMENTED LATTICES
topic ANNIHILATOR
CONGRUENCES
NORMAL LATTICES
PRIESTLEY SPACES
QUASICOMPLEMENTED LATTICES
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 this note we shall give some results on annihilators preserving congruence relations, or AP-congruences, in bounded distributive lattices. We shall give some new characterizations, and a topological interpretation of the notion of annihilator preserving congruences introduced in [JANOWITZ, M. F.: Annihilator preserving congruence relations of lattices, Algebra Universalis 5 (1975), 391–394]. As an application of these results, we shall prove that the quotient of a quasicomplemented lattice by means of a AP-congruence is a quasicomplemented lattice. Similarly, we will prove that the quotient of a normal latttice by means of a AP-congruence is also a normal lattice.
Fil: Celani, Sergio Arturo. Universidad Nacional del Centro de la Provincia de Buenos Aires. Facultad de Ciencias Exactas. Núcleo Consolidado de Matemática Pura y Aplicada; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Tandil; Argentina
description In this note we shall give some results on annihilators preserving congruence relations, or AP-congruences, in bounded distributive lattices. We shall give some new characterizations, and a topological interpretation of the notion of annihilator preserving congruences introduced in [JANOWITZ, M. F.: Annihilator preserving congruence relations of lattices, Algebra Universalis 5 (1975), 391–394]. As an application of these results, we shall prove that the quotient of a quasicomplemented lattice by means of a AP-congruence is a quasicomplemented lattice. Similarly, we will prove that the quotient of a normal latttice by means of a AP-congruence is also a normal lattice.
publishDate 2012
dc.date.none.fl_str_mv 2012-05
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/11336/208810
Celani, Sergio Arturo; Remarks on annihilators preserving congruence relations; Versita; Mathematica Slovaca; 62; 3; 5-2012; 389-398
0139-9918
CONICET Digital
CONICET
url http://hdl.handle.net/11336/208810
identifier_str_mv Celani, Sergio Arturo; Remarks on annihilators preserving congruence relations; Versita; Mathematica Slovaca; 62; 3; 5-2012; 389-398
0139-9918
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/10.2478/s12175-012-0016-y
info:eu-repo/semantics/altIdentifier/doi/10.2478/s12175-012-0016-y
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 Versita
publisher.none.fl_str_mv Versita
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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