zbMATH — the first resource for mathematics

Degree bounds for the division problem in polynomial ideals. (English) Zbl 0691.12010
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 $$g_ i\leq \delta$$.
Reviewer: Xu Yonghua

MSC:
 12E05 Polynomials in general fields (irreducibility, etc.) 13F20 Polynomial rings and ideals; rings of integer-valued polynomials
Keywords:
degree of polynomial
Full Text: