If 
is a Noetherian ring, then ![S=R[X]](/images/equations/HilbertBasisTheorem/Inline2.svg)
is also a Noetherian ring.
Hilbert Basis Theorem
See also
Algebraic Variety, Fundamental System, Noetherian Ring, SyzygyExplore with Wolfram|Alpha
References
Hilbert, D. "Über die Theorie der algebraischen Formen." Math. Ann. 36, 473-534, 1890.Referenced on Wolfram|Alpha
Hilbert Basis TheoremCite this as:
Weisstein, Eric W. "Hilbert Basis Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/HilbertBasisTheorem.html