Degree bounds for the division problem in polynomial ideals (Q582326)

Let \(f_ 1,...,f_ m\) be polynomials in n variables of degree at most D over an arbitrary field, and let I be the ideal they generate. The author gives an estimate of the smallest integer \(\delta\) such that for any \(P\in I\), we can write \(P=f_ 1g_ 1+...+f_ mg_ m\) with deg \(g_ i\leq \delta\).