Intersections of sequences of ideals generated by polynomials
type: Item
instance of: scholarly article
title: Intersections of sequences of ideals generated by polynomials
zbMATH Open document ID: 0942.13024
DOI: 10.1016/S0022-4049(98)00025-5
author: T. Winiarski
author: Joachim Apel
author: J. Stückrad
author: Piotr Tworzewski
published in: Journal of Pure and Applied Algebra
publication date: 1999-08-19T00:00:00Z
review text: The main result of the paper gives the reduced Gröbner basis with respect to an admissible term of order type \(\omega\) of the intersection of a descending chain of polynomial ideals. It is also shown that the result does not hold for any admissible order. Using this and previous results of \textit{P. Gianni, B. Trager} and \textit{G. Zacharias} [J. Symb. Comput. 6, No. 2/3, 149-167 (1988; Zbl 0667.13008)], one can compute a generating set for arbitrary intersections. The authors apply their main theorem to Lagrange interpolation on algebraic sets, obtaining the ideal \(I\) of an algebraic set as the intersection of zero-dimensional ideals whose affine Hilbert functions converge towards the affine Hilbert function of \(I\).
reviewed by: Mihai Cipu
Mathematics Subject Classification ID: 13P10
Mathematics Subject Classification ID: 14A05
Mathematics Subject Classification ID: 41A65
Mathematics Subject Classification ID: 13D40
zbMATH DE Number: 1308223
zbMATH Keywords: reduced Gröbner basis
zbMATH Keywords: admissible term order of order type \(\omega\)
zbMATH Keywords: Lagrange interpolation on algebraic sets
zbMATH Keywords: ideal of an algebraic set
zbMATH Keywords: affine Hilbert functions
MaRDI profile type: Publication
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full work available at URL: s0022-4049(98)00025-5
OpenAlex ID: W2065590164
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description: scientific article; zbMATH DE number 1308223