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Residue calculus and effective Nullstellensatz. (English) Zbl 0944.14002
Let $$A$$ be an integral factorial regular ring with infinite quotient field $$K$$ and equipped with a size (the typical examples are $$\mathbb{Z}$$ and $$\mathbb{F}_p [y_1,\dots, y_q]$$). Using multivariate residue calculus, the authors are studying the Bézout identity and consequently the effective Nullstellensatz in $$K[X_1,\dots, X_n]$$. This provides sharp size estimates for the denominator and the “divisors” in the Bézout identity. The results obtained here improve the estimates obtained in the case $$A=\mathbb{Z}$$ by the same authors in a previous work [C. A. Berenstein and A. Yger, Acta Math. 166, No. 1/2, 69-120 (1991; Zbl 0724.32002)].

##### MSC:
 14A05 Relevant commutative algebra 13F20 Polynomial rings and ideals; rings of integer-valued polynomials
##### Keywords:
effective Nullstellensatz; Bézout identity
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