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Let $\K$ be a commutative field, an algorithmic approach to residue symbols defined on a Noetherian $\K$@-algebra $\R$ has been developed. It is used to prove an effective Nullstellensatz for polynomials defined over infinite factorial rings $\A$ equipped with a size. This result extends (and slightly improves) the previous work of the authors in the case $\A=\Z$.

Copyright American Mathematical Society 1996

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Article Info

• ERA Amer. Math. Soc. 02 (1996), pp. 82-91
• Publisher Identifier: S 1079-6762(96)00011-10
• 1991 Mathematics Subject Classification. Primary 14Q20; Secondary 13F20, 14C17, 32C30
• Received by the editors April 15, 1996
• Communicated by Robert Lazarsfeld
• Comments (When Available)

Carlos A. Berenstein

Institute for Systems Research, University of Maryland, College Park, MD 20742

E-mail address: carlos@src.umd.edu

Alain Yger

Laboratoire de Mathématiques Pures, Université Bordeaux Sciences, 33405 Talence, France

E-mail address: yger@math.u-bordeaux.fr

This research has been partially supported by grants from NSA and NSF