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Krick, T.; Sabia, J.; Solernó, P. "On intrinsic bounds in the Nullstellensatz" (1997) Applicable Algebra in Engineering, Communications and Computing. 8(2):125-134
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Abstract:

Let k be a field and f1 , . . . , fs be non constant polynomials in k[X1 , . . . , Xn] which generate the trivial ideal. In this paper we define an invariant associated to the sequence f1 , . . . , fs: the geometric degree of the system. With this notion we can show the following effective Nullstellensatz: if δ denotes the geometric degree of the trivial system f1 , . . .. , fs and d:= maxjdeg(fj), then there exist polynomials p1 , . . . , ps ∈ k[X1 , . . . , Xn] such that 1 = ∑jpjfjand deg pjfj ≦ 3n2δd. Since the number δ is always bounded by (d + 1)n-1, one deduces a classical single exponential upper bound in terms of d and n, but in some cases our new bound improves the known ones.

Registro:

Documento: Artículo
Título:On intrinsic bounds in the Nullstellensatz
Autor:Krick, T.; Sabia, J.; Solernó, P.
Filiación:Departamento de Matemática, Fac. de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428- Buenos Aires, Argentina
Depto. de Economía y Matemat., Universidad de San Andrés, Vito Dumas 284, 1644- Victoria, Buenos Aires, Argentina
Palabras clave:Complete intersection polynomial ideals; Effective Nullstellensatz; Geometric degree; Trace theory; Functions; Geometry; Number theory; Set theory; Geometric degree; Hilbert Nullstellensatz; Trace theory; Polynomials
Año:1997
Volumen:8
Número:2
Página de inicio:125
Página de fin:134
DOI: http://dx.doi.org/10.1007/s002000050057
Título revista:Applicable Algebra in Engineering, Communications and Computing
Título revista abreviado:Appl Algebra Eng Commun Comput
ISSN:09381279
CODEN:AAECE
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09381279_v8_n2_p125_Krick

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Citas:

---------- APA ----------
Krick, T., Sabia, J. & Solernó, P. (1997) . On intrinsic bounds in the Nullstellensatz. Applicable Algebra in Engineering, Communications and Computing, 8(2), 125-134.
http://dx.doi.org/10.1007/s002000050057
---------- CHICAGO ----------
Krick, T., Sabia, J., Solernó, P. "On intrinsic bounds in the Nullstellensatz" . Applicable Algebra in Engineering, Communications and Computing 8, no. 2 (1997) : 125-134.
http://dx.doi.org/10.1007/s002000050057
---------- MLA ----------
Krick, T., Sabia, J., Solernó, P. "On intrinsic bounds in the Nullstellensatz" . Applicable Algebra in Engineering, Communications and Computing, vol. 8, no. 2, 1997, pp. 125-134.
http://dx.doi.org/10.1007/s002000050057
---------- VANCOUVER ----------
Krick, T., Sabia, J., Solernó, P. On intrinsic bounds in the Nullstellensatz. Appl Algebra Eng Commun Comput. 1997;8(2):125-134.
http://dx.doi.org/10.1007/s002000050057