Intersections of sequences of ideals generated by polynomials

Abstract

We present a method for determining the reduced Gröbner basis with respect to a given admissible term order of order type ω of the intersection ideal of an infinite sequence of polynomial ideals. As an application we discuss the Lagrange type interpolation on algebraic sets and the “approximation” of the ideal I of an algebraic set by zero dimensional ideals, whose affine Hilbert functions converge towards the affine Hilbert function of I.