Redirected from Hilbert basis theorem
Hilbert produced an innovative proof by contradiction using mathematical induction; his method does not give an algorithm to produce the finitely many basis polynomials for a given ideal: it only shows that they must exist. One can determine basis polynomials using the method of Gröbner bases[?].
A slightly more general statement of Hilbert's basis theorem is: if R is a left (respectively right) Noetherian ring, then the polynomial ring R[X] is also left (respectively right) Noetherian.
The Mizar project has completely formalized and automatically checked a proof of Hilbert's basis theorem in the HILBASIS file (http://www.mizar.org/JFM/Vol12/hilbasis).
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