Let be an algebraically closed field and let be an ideal in , where is a finite set of indeterminates. Let be such that for any in , if every element of vanishes when evaluated if we set each (), then also vanishes. Then lies in for some . Colloquially, the theory of algebraically closed fields is a complete model.
Hilbert's Nullstellensatz
See also
Algebraic Set, IdealExplore with Wolfram|Alpha
References
Becker, T. and Weispfenning, V. "The Hilbert Nullstellensatz." §7.4 in Gröbner Bases: A Computational Approach to Commutative Algebra. New York: Springer-Verlag, pp. 312-323, 1993.Hartshorne, R. Algebraic Geometry. New York: Springer-Verlag, 1977.Referenced on Wolfram|Alpha
Hilbert's NullstellensatzCite this as:
Weisstein, Eric W. "Hilbert's Nullstellensatz." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/HilbertsNullstellensatz.html