# Hilbert's theorem

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**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
- 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 irreducibility theorem, in number theory, concerning irreducible polynomials
- Hilbert's Nullstellensatz, the basis of abstract algebra, 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