an:01339466
Zbl 0944.14002
Berenstein, Carlos A.; Yger, Alain
Residue calculus and effective Nullstellensatz
EN
Am. J. Math. 121, No. 4, 723-796 (1999).
00057565
1999
j
14A05 13F20
effective Nullstellensatz; B??zout identity
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 B??zout 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 B??zout identity. The results obtained here improve the estimates obtained in the case \(A=\mathbb{Z}\) by the same authors in a previous work [\textit{C. A. Berenstein} and \textit{A. Yger}, Acta Math. 166, No. 1/2, 69-120 (1991; Zbl 0724.32002)].
Christodor-Paul Ionescu (Bucure??ti)
Zbl 0724.32002