About: Hilbert's irreducibility theorem

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In number theory, Hilbert's irreducibility theorem, conceived by David Hilbert in 1892, states that every finite set of irreducible polynomials in a finite number of variables and having rational number coefficients admit a common specialization of a proper subset of the variables to rational numbers such that all the polynomials remain irreducible. This theorem is a prominent theorem in number theory.

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rdfs:label	Irreduzibilitätssatz von Hilbert (de) Théorème d'irréductibilité de Hilbert (fr) Hilbert's irreducibility theorem (en)
rdfs:comment	Der Irreduzibilitätssatz von Hilbert ist ein Satz von David Hilbert über die Irreduzibilität von Polynomen mit rationalen Koeffizienten in mehreren Variablen, wenn eine Anzahl der Variablen rationale Werte erhalten. Verallgemeinerungen des Satzes betreffen Polynome über anderen Körpern als den rationalen Zahlen. Der Satz ist von besonderer Bedeutung für die Zahlentheorie und die arithmetische algebraische Geometrie. (de) In number theory, Hilbert's irreducibility theorem, conceived by David Hilbert in 1892, states that every finite set of irreducible polynomials in a finite number of variables and having rational number coefficients admit a common specialization of a proper subset of the variables to rational numbers such that all the polynomials remain irreducible. This theorem is a prominent theorem in number theory. (en) En théorie des nombres, le théorème d'irréductibilité de Hilbert, conçu par David Hilbert en 1892, stipule que tout ensemble fini de polynômes irréductibles en plusieurs variables et à coefficients rationnels admet une spécialisation commune d'un sous-ensemble propre des variables en des rationnels tels que tous ces polynômes restent irréductibles. Sur le cas le plus simple, si P(X, Y) est un polynôme irréductible de Q[X, Y], alors il existe t rationnel tel que P(t, Y) soit irréductible dans Q[Y]. Ce théorème joue un rôle important en théorie des nombres. (fr)
dcterms:subject	Theorems in number theory Theorems about polynomials David Hilbert
Wikipage page ID	1951153 (xsd:integer)
Wikipage revision ID	1039731967 (xsd:integer)
Link from a Wikipage to another Wikipage	David Hilbert Inverse Galois problem Theorems in number theory Thin set (Serre) Andrew Wiles Irreducible polynomial Absolutely irreducible Algebra Algebraic geometry Fermat's Last Theorem Number field Number theory Theorems about polynomials David Hilbert Rational number Zariski topology Springer-Verlag Hilbertian field
sameAs	Hilbert's irreducibility theorem Hilbert's irreducibility theorem Hilbert's irreducibility theorem Hilbert's irreducibility theorem Hilbert's irreducibility theorem Hilbert's irreducibility theorem
dbp:wikiPageUsesTemplate	dbt:Cite_book dbt:More_footnotes dbt:Reflist dbt:Short_description
has abstract	Der Irreduzibilitätssatz von Hilbert ist ein Satz von David Hilbert über die Irreduzibilität von Polynomen mit rationalen Koeffizienten in mehreren Variablen, wenn eine Anzahl der Variablen rationale Werte erhalten. Verallgemeinerungen des Satzes betreffen Polynome über anderen Körpern als den rationalen Zahlen. Der Satz ist von besonderer Bedeutung für die Zahlentheorie und die arithmetische algebraische Geometrie. (de) In number theory, Hilbert's irreducibility theorem, conceived by David Hilbert in 1892, states that every finite set of irreducible polynomials in a finite number of variables and having rational number coefficients admit a common specialization of a proper subset of the variables to rational numbers such that all the polynomials remain irreducible. This theorem is a prominent theorem in number theory. (en) En théorie des nombres, le théorème d'irréductibilité de Hilbert, conçu par David Hilbert en 1892, stipule que tout ensemble fini de polynômes irréductibles en plusieurs variables et à coefficients rationnels admet une spécialisation commune d'un sous-ensemble propre des variables en des rationnels tels que tous ces polynômes restent irréductibles. Sur le cas le plus simple, si P(X, Y) est un polynôme irréductible de Q[X, Y], alors il existe t rationnel tel que P(t, Y) soit irréductible dans Q[Y]. Ce théorème joue un rôle important en théorie des nombres. (fr)
prov:wasDerivedFrom	wikipedia-en:Hilbert's_irreducibility_theorem?oldid=1039731967&ns=0
page length (characters) of wiki page	4569 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Hilbert's_irreducibility_theorem
is Link from a Wikipage to another Wikipage of	David Hilbert Inverse Galois problem List of scientific laws named after people Glossary of arithmetic and diophantine geometry Thin set (Serre) Irreducible polynomial Diophantine geometry Glossary of field theory Haran's diamond theorem Séminaire Nicolas Bourbaki (1950–1959) Hilbert's theorem List of theorems List of things named after David Hilbert Hilbert irreducibility theorem
is Wikipage redirect of	Hilbert irreducibility theorem
is foaf:primaryTopic of	wikipedia-en:Hilbert's_irreducibility_theorem

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