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