Normalization of Rings

Autores
Greuel, Gert Martin; Laplagne, Santiago Jorge; Seelisch, Frank
Año de publicación
2010
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We present a new algorithm to compute the integral closure of a reduced Noetherian ring in its total ring of fractions. A modification, applicable in positive characteristic, where actually all computations are over the original ring, is also described. The new algorithm of this paper has been implemented in Singular, for localizations of affine rings with respect to arbitrary monomial orderings. Benchmark tests show that it is in general much faster than any other implementation of normalization algorithms known to us.
Fil: Greuel, Gert Martin. University of Kaiserslautern; Alemania
Fil: Laplagne, Santiago Jorge. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Seelisch, Frank. University of Kaiserslautern; Alemania
Materia
Normalization
Integral Closure
Test Ideal
Grauert-Remmert Criterion
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/16532
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/16532
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Normalization of RingsGreuel, Gert MartinLaplagne, Santiago JorgeSeelisch, FrankNormalizationIntegral ClosureTest IdealGrauert-Remmert Criterionhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We present a new algorithm to compute the integral closure of a reduced Noetherian ring in its total ring of fractions. A modification, applicable in positive characteristic, where actually all computations are over the original ring, is also described. The new algorithm of this paper has been implemented in Singular, for localizations of affine rings with respect to arbitrary monomial orderings. Benchmark tests show that it is in general much faster than any other implementation of normalization algorithms known to us.Fil: Greuel, Gert Martin. University of Kaiserslautern; AlemaniaFil: Laplagne, Santiago Jorge. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Seelisch, Frank. University of Kaiserslautern; AlemaniaElsevier2010-08info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/16532Greuel, Gert Martin; Laplagne, Santiago Jorge; Seelisch, Frank; Normalization of Rings; Elsevier; Journal Of Symbolic Computation; 45; 9; 8-2010; 887-9010747-7171enginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.jsc.2010.04.002info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0747717110000611info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:03:46Zoai:ri.conicet.gov.ar:11336/16532instacron: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:34982025-10-22 11:03:46.332CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Normalization of Rings
title Normalization of Rings
spellingShingle Normalization of Rings
Greuel, Gert Martin
Normalization
Integral Closure
Test Ideal
Grauert-Remmert Criterion
title_short Normalization of Rings
title_full Normalization of Rings
title_fullStr Normalization of Rings
title_full_unstemmed Normalization of Rings
title_sort Normalization of Rings
dc.creator.none.fl_str_mv Greuel, Gert Martin
Laplagne, Santiago Jorge
Seelisch, Frank
author Greuel, Gert Martin
author_facet Greuel, Gert Martin
Laplagne, Santiago Jorge
Seelisch, Frank
author_role author
author2 Laplagne, Santiago Jorge
Seelisch, Frank
author2_role author
author
dc.subject.none.fl_str_mv Normalization
Integral Closure
Test Ideal
Grauert-Remmert Criterion
topic Normalization
Integral Closure
Test Ideal
Grauert-Remmert Criterion
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 present a new algorithm to compute the integral closure of a reduced Noetherian ring in its total ring of fractions. A modification, applicable in positive characteristic, where actually all computations are over the original ring, is also described. The new algorithm of this paper has been implemented in Singular, for localizations of affine rings with respect to arbitrary monomial orderings. Benchmark tests show that it is in general much faster than any other implementation of normalization algorithms known to us.
Fil: Greuel, Gert Martin. University of Kaiserslautern; Alemania
Fil: Laplagne, Santiago Jorge. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Seelisch, Frank. University of Kaiserslautern; Alemania
description We present a new algorithm to compute the integral closure of a reduced Noetherian ring in its total ring of fractions. A modification, applicable in positive characteristic, where actually all computations are over the original ring, is also described. The new algorithm of this paper has been implemented in Singular, for localizations of affine rings with respect to arbitrary monomial orderings. Benchmark tests show that it is in general much faster than any other implementation of normalization algorithms known to us.
publishDate 2010
dc.date.none.fl_str_mv 2010-08
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/11336/16532
Greuel, Gert Martin; Laplagne, Santiago Jorge; Seelisch, Frank; Normalization of Rings; Elsevier; Journal Of Symbolic Computation; 45; 9; 8-2010; 887-901
0747-7171
url http://hdl.handle.net/11336/16532
identifier_str_mv Greuel, Gert Martin; Laplagne, Santiago Jorge; Seelisch, Frank; Normalization of Rings; Elsevier; Journal Of Symbolic Computation; 45; 9; 8-2010; 887-901
0747-7171
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jsc.2010.04.002
info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0747717110000611
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
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 12.982451

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