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- Hilbert's_basis_theorem abstract "In mathematics, specifically commutative algebra, Hilbert's basis theorem states that every ideal in the ring of multivariate polynomials over a Noetherian ring is finitely generated. This can be translated into algebraic geometry as follows: every algebraic set over a field can be described as the set of common roots of finitely many polynomial equations. Hilbert (1890) proved the theorem (for the special case of polynomial rings over a field) in the course of his proof of finite generation of rings of invariants. 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.".
- Hilbert's_basis_theorem wikiPageExternalLink hilbasis.html.
- Hilbert's_basis_theorem wikiPageID "13733".
- Hilbert's_basis_theorem wikiPageRevisionID "598086314".
- Hilbert's_basis_theorem hasPhotoCollection Hilbert's_basis_theorem.
- Hilbert's_basis_theorem subject Category:Articles_containing_proofs.
- Hilbert's_basis_theorem subject Category:Commutative_algebra.
- Hilbert's_basis_theorem subject Category:Invariant_theory.
- Hilbert's_basis_theorem subject Category:Theorems_in_abstract_algebra.
- Hilbert's_basis_theorem type Abstraction100002137.
- Hilbert's_basis_theorem type Communication100033020.
- Hilbert's_basis_theorem type Message106598915.
- Hilbert's_basis_theorem type Proposition106750804.
- Hilbert's_basis_theorem type Statement106722453.
- Hilbert's_basis_theorem type Theorem106752293.
- Hilbert's_basis_theorem type TheoremsInAbstractAlgebra.
- Hilbert's_basis_theorem type TheoremsInAlgebra.
- Hilbert's_basis_theorem comment "In mathematics, specifically commutative algebra, Hilbert's basis theorem states that every ideal in the ring of multivariate polynomials over a Noetherian ring is finitely generated. This can be translated into algebraic geometry as follows: every algebraic set over a field can be described as the set of common roots of finitely many polynomial equations.".
- Hilbert's_basis_theorem label "Basisstelling van Hilbert".
- Hilbert's_basis_theorem label "Hilbert's basis theorem".
- Hilbert's_basis_theorem label "Hilbertscher Basissatz".
- Hilbert's_basis_theorem label "Teorema da base de Hilbert".
- Hilbert's_basis_theorem label "Teorema de la base de Hilbert".
- Hilbert's_basis_theorem label "Teorema della base di Hilbert".
- Hilbert's_basis_theorem label "Théorème de la base de Hilbert".
- Hilbert's_basis_theorem label "Twierdzenie Hilberta o bazie".
- Hilbert's_basis_theorem label "Теорема Гильберта о базисе".
- Hilbert's_basis_theorem sameAs Hilbertova_věta_o_bázi.
- Hilbert's_basis_theorem sameAs Hilbertscher_Basissatz.
- Hilbert's_basis_theorem sameAs Teorema_de_la_base_de_Hilbert.
- Hilbert's_basis_theorem sameAs Théorème_de_la_base_de_Hilbert.
- Hilbert's_basis_theorem sameAs Teorema_della_base_di_Hilbert.
- Hilbert's_basis_theorem sameAs Basisstelling_van_Hilbert.
- Hilbert's_basis_theorem sameAs Twierdzenie_Hilberta_o_bazie.
- Hilbert's_basis_theorem sameAs Teorema_da_base_de_Hilbert.
- Hilbert's_basis_theorem sameAs m.03ks0.
- Hilbert's_basis_theorem sameAs Q656645.
- Hilbert's_basis_theorem sameAs Q656645.
- Hilbert's_basis_theorem sameAs Hilbert's_basis_theorem.
- Hilbert's_basis_theorem wasDerivedFrom Hilbert's_basis_theorem?oldid=598086314.
- Hilbert's_basis_theorem isPrimaryTopicOf Hilbert's_basis_theorem.