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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
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
Palabras clave:Differential algebra; Differentiation index; Lüroth's Theorem
Año:2018
Volumen:507
Página de inicio:547
Página de fin:570
DOI: http://dx.doi.org/10.1016/j.jalgebra.2018.01.050
Título revista:Journal of Algebra
Título revista abreviado:J. Algebra
ISSN:00218693
CODEN:JALGA
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00218693_v507_n_p547_DAlfonso

Referencias:

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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