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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
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