A note on upper bounds for ideal-theoretic problems

Abstract

An upper bound of d 2x with x = n (log 3)/(log 4) is given for the generators of the module of the relations (syzygies) between a finite set of polynomials in n variables, of degree at most d , over a field. A similar bound with x = n (log 3)/(log 4) + O(log n ) is deduced for a membership relation between a polynomial and an ideal given by generators.