Abstract:
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. © 2018 Elsevier Inc.
Registro:
Documento: |
Artículo
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Título: | Quantitative aspects of the generalized differential Lüroth's Theorem |
Autor: | D'Alfonso, L.; Jeronimo, G.; Solernó, P. |
Filiación: | Universidad de Buenos Aires, Ciclo Básico Común, Departamento de Ciencias Exactas, Área Matemática, Buenos Aires, Argentina Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Departamento de Matemática, Buenos Aires, Argentina Universidad de Buenos Aires, Consejo Nacional de Investigaciones Científicas y Técnicas, Instituto de Investigaciones Matemáticas Luis A. Santaló (IMAS), Buenos Aires, Argentina
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Palabras clave: | Differential algebra; Differentiation index; Lüroth's Theorem |
Año: | 2018
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Volumen: | 507
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Página de inicio: | 547
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Página de fin: | 570
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DOI: |
http://dx.doi.org/10.1016/j.jalgebra.2018.01.050 |
Título revista: | Journal of Algebra
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Título revista abreviado: | J. Algebra
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ISSN: | 00218693
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CODEN: | JALGA
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Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00218693_v507_n_p547_DAlfonso |
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Citas:
---------- APA ----------
D'Alfonso, L., Jeronimo, G. & Solernó, P.
(2018)
. Quantitative aspects of the generalized differential Lüroth's Theorem. Journal of Algebra, 507, 547-570.
http://dx.doi.org/10.1016/j.jalgebra.2018.01.050---------- CHICAGO ----------
D'Alfonso, L., Jeronimo, G., Solernó, P.
"Quantitative aspects of the generalized differential Lüroth's Theorem"
. Journal of Algebra 507
(2018) : 547-570.
http://dx.doi.org/10.1016/j.jalgebra.2018.01.050---------- MLA ----------
D'Alfonso, L., Jeronimo, G., Solernó, P.
"Quantitative aspects of the generalized differential Lüroth's Theorem"
. Journal of Algebra, vol. 507, 2018, pp. 547-570.
http://dx.doi.org/10.1016/j.jalgebra.2018.01.050---------- VANCOUVER ----------
D'Alfonso, L., Jeronimo, G., Solernó, P. Quantitative aspects of the generalized differential Lüroth's Theorem. J. Algebra. 2018;507:547-570.
http://dx.doi.org/10.1016/j.jalgebra.2018.01.050