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Residues and effective Nullstellensatz

Author(s): Carlos A. Berenstein; Alain Yger
Journal: Electron. Res. Announc. Amer. Math. Soc. 2 (1996), 82-91.
MSC (1991): Primary 14Q20; Secondary 13F20, 14C17, 32C30
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Abstract: Let $\mathbf {K} $ be a commutative field; an algorithmic approach to residue symbols defined on a Noetherian $\mathbf {K} $-algebra $\mathbf {R} $ has been developed. It is used to prove an effective Nullstellensatz for polynomials defined over infinite factorial rings $\mathbf { A} $ equipped with a size. This result extends (and slightly improves) the previous work of the authors in the case $\mathbf { A} =\mathbf {Z} $.

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Additional Information:

Carlos A. Berenstein
Affiliation: Institute for Systems Research, University of Maryland, College Park, MD 20742
Email: carlos@src.umd.edu

Alain Yger
Affiliation: Laboratoire de Mathématiques Pures, Université Bordeaux Sciences, 33405 Talence, France
Email: yger@math.u-bordeaux.fr

DOI: 10.1090/S1079-6762-96-00011-X
PII: S 1079-6762(96)00011-X
Keywords: Effective Nullstellensatz, residues, arithmetic B\'{e}zout theory
Received by editor(s): April 15, 1996
Additional Notes: This research has been partially supported by grants from NSA and NSF
Communicated by: Robert Lazarsfeld
Copyright of article: Copyright 1996, American Mathematical Society

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