title: Hilbert's theorem
text: # Hilbert's theorem
  
  Hilbert's theorem may refer to:
  
  * Hilbert's theorem (differential geometry), stating there exists no complete regular surface of constant negative gaussian curvature immersed in $\mathbb {R} ^{3}$
  * Hilbert's Theorem 90, an important result on cyclic extensions of fields that leads to Kummer theory
  * Hilbert's basis theorem, in commutative algebra, stating every ideal in the ring of multivariate polynomials over a Noetherian ring is finitely generated
  * Hilbert's finiteness theorem, in invariant theory, stating that the ring of invariants of a reductive group is finitely generated
  * Hilbert's irreducibility theorem, in number theory, concerning irreducible polynomials
  * Hilbert's Nullstellensatz, the basis of algebraic geometry, establishing a fundamental relationship between geometry and algebra
  * Hilbert's syzygy theorem, a result of commutative algebra in connection with the syzygy problem of invariant theory
  