Quantitative aspects of the generalized differential Lüroth's Theorem

Autores
D'Alfonso, Lisi; Jeronimo, Gabriela Tali; Solernó, Pablo Luis
Año de publicación
2018
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Let F be a differential field of characteristic 0, t=t1,…,tm a finite set of differential indeterminates over F and G⊂F〈t〉 a differential field extension of F, generated by nonconstant rational functions α1,…,αn of total degree and order bounded by d and e≥1 respectively. The generalized differential Lüroth's Theorem states that if the differential transcendence degree of G over F is 1, there exists v∈G such that G=F〈v〉. We prove a new explicit upper bound for the degree of v in terms of n,m,d and e. Further, we exhibit an effective procedure to compute v.
Fil: D'Alfonso, Lisi. Universidad de Buenos Aires. Ciclo Básico Común; Argentina
Fil: Jeronimo, Gabriela Tali. Universidad de Buenos Aires. Ciclo Básico Común; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Solernó, Pablo Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Materia
DIFFERENTIAL ALGEBRA
DIFFERENTIATION INDEX
LÜROTH'S THEOREM
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:11336/89718
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Quantitative aspects of the generalized differential Lüroth's TheoremD'Alfonso, LisiJeronimo, Gabriela TaliSolernó, Pablo LuisDIFFERENTIAL ALGEBRADIFFERENTIATION INDEXLÜROTH'S THEOREMhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Let F be a differential field of characteristic 0, t=t1,…,tm a finite set of differential indeterminates over F and G⊂F〈t〉 a differential field extension of F, generated by nonconstant rational functions α1,…,αn of total degree and order bounded by d and e≥1 respectively. The generalized differential Lüroth's Theorem states that if the differential transcendence degree of G over F is 1, there exists v∈G such that G=F〈v〉. We prove a new explicit upper bound for the degree of v in terms of n,m,d and e. Further, we exhibit an effective procedure to compute v.Fil: D'Alfonso, Lisi. Universidad de Buenos Aires. Ciclo Básico Común; ArgentinaFil: Jeronimo, Gabriela Tali. Universidad de Buenos Aires. Ciclo Básico Común; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Solernó, Pablo Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaAcademic Press Inc Elsevier Science2018-08-01info: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/11336/89718D'Alfonso, Lisi; Jeronimo, Gabriela Tali; Solernó, Pablo Luis; Quantitative aspects of the generalized differential Lüroth's Theorem; Academic Press Inc Elsevier Science; Journal of Algebra; 507; 01-8-2018; 547-5700021-8693CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0021869318301492info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jalgebra.2018.01.050info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-17T11:14:12Zoai:ri.conicet.gov.ar:11336/89718instacron: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:34982025-09-17 11:14:13.002CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Quantitative aspects of the generalized differential Lüroth's Theorem
title Quantitative aspects of the generalized differential Lüroth's Theorem
spellingShingle Quantitative aspects of the generalized differential Lüroth's Theorem
D'Alfonso, Lisi
DIFFERENTIAL ALGEBRA
DIFFERENTIATION INDEX
LÜROTH'S THEOREM
title_short Quantitative aspects of the generalized differential Lüroth's Theorem
title_full Quantitative aspects of the generalized differential Lüroth's Theorem
title_fullStr Quantitative aspects of the generalized differential Lüroth's Theorem
title_full_unstemmed Quantitative aspects of the generalized differential Lüroth's Theorem
title_sort Quantitative aspects of the generalized differential Lüroth's Theorem
dc.creator.none.fl_str_mv D'Alfonso, Lisi
Jeronimo, Gabriela Tali
Solernó, Pablo Luis
author D'Alfonso, Lisi
author_facet D'Alfonso, Lisi
Jeronimo, Gabriela Tali
Solernó, Pablo Luis
author_role author
author2 Jeronimo, Gabriela Tali
Solernó, Pablo Luis
author2_role author
author
dc.subject.none.fl_str_mv DIFFERENTIAL ALGEBRA
DIFFERENTIATION INDEX
LÜROTH'S THEOREM
topic DIFFERENTIAL ALGEBRA
DIFFERENTIATION INDEX
LÜROTH'S THEOREM
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Let F be a differential field of characteristic 0, t=t1,…,tm a finite set of differential indeterminates over F and G⊂F〈t〉 a differential field extension of F, generated by nonconstant rational functions α1,…,αn of total degree and order bounded by d and e≥1 respectively. The generalized differential Lüroth's Theorem states that if the differential transcendence degree of G over F is 1, there exists v∈G such that G=F〈v〉. We prove a new explicit upper bound for the degree of v in terms of n,m,d and e. Further, we exhibit an effective procedure to compute v.
Fil: D'Alfonso, Lisi. Universidad de Buenos Aires. Ciclo Básico Común; Argentina
Fil: Jeronimo, Gabriela Tali. Universidad de Buenos Aires. Ciclo Básico Común; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Solernó, Pablo Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
description Let F be a differential field of characteristic 0, t=t1,…,tm a finite set of differential indeterminates over F and G⊂F〈t〉 a differential field extension of F, generated by nonconstant rational functions α1,…,αn of total degree and order bounded by d and e≥1 respectively. The generalized differential Lüroth's Theorem states that if the differential transcendence degree of G over F is 1, there exists v∈G such that G=F〈v〉. We prove a new explicit upper bound for the degree of v in terms of n,m,d and e. Further, we exhibit an effective procedure to compute v.
publishDate 2018
dc.date.none.fl_str_mv 2018-08-01
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/11336/89718
D'Alfonso, Lisi; Jeronimo, Gabriela Tali; Solernó, Pablo Luis; Quantitative aspects of the generalized differential Lüroth's Theorem; Academic Press Inc Elsevier Science; Journal of Algebra; 507; 01-8-2018; 547-570
0021-8693
CONICET Digital
CONICET
url http://hdl.handle.net/11336/89718
identifier_str_mv D'Alfonso, Lisi; Jeronimo, Gabriela Tali; Solernó, Pablo Luis; Quantitative aspects of the generalized differential Lüroth's Theorem; Academic Press Inc Elsevier Science; Journal of Algebra; 507; 01-8-2018; 547-570
0021-8693
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://www.sciencedirect.com/science/article/pii/S0021869318301492
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jalgebra.2018.01.050
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
dc.publisher.none.fl_str_mv Academic Press Inc Elsevier Science
publisher.none.fl_str_mv Academic Press Inc Elsevier Science
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 13.001348

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