Reduction of power series in a polydisc with respect to a Gröbner basis

• Autorzy: Szpond J.

Identyfikatory

DOI

10.4064/ba53-2-3

• Języki publikacji: EN

Abstrakty

EN

We deal with a reduction of power series convergent in a polydisc with respect to a Gröbner basis of a polynomial ideal. The results are applied to proving that a Nash function whose graph is algebraic in a “large enough” polydisc, must be a polynomial. Moreover, we give an effective method for finding this polydisc.

Słowa kluczowe

EN

Gröbner basis; polynomial ideals; power series; Nash function

PL

ideał wielomianowy; szereg potęgowy; funkcja Nasha

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2005
• Tom: Vol. 53, no 2
• Strony: 137--145
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Szpond J.

• Institute of Mathematics, Pedagogical University, Podchorążych 2, 30-084 Kraków, Poland,

Bibliografia

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• [3] T. Becker and V. Weispfenning, Gröbner Bases, a Computational Approach to Commutative Algebra, Springer, 1993.
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• [5] H. Grauert und R. Remmert, Analytische Stellenalgebren, Springer, 1971.
• [6] G. M. Greuel and G. Pfister, A Singular Introduction to Commutative Algebra, Springer, 2002.
• [7] W. Rudin, A geometric criterion for algebraic varieties, J. Math. Mech. 17 (1968), 671-683.
• [8] J.-P. Serre, Géométrie alqébrique et Géométrie analytique, Ann. Inst. Fourier (Grenoble) 6 (1955-1956), 1-42.
• [9] P. Tworzewski, Intersections of analytic sets with linear subspaces, Ann. Scuola Norm. Sup. Pisa 17 (1990), 227-271.