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dbr:David_Hilbert
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dbr:Hilbert's_irreducibility_theorem
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yago:Relation100031921 yago:Proposition106750804 yago:WikicatTheoremsInNumberTheory yago:Abstraction100002137 yago:Message106598915 yago:Polynomial105861855 yago:Communication100033020 yago:WikicatPolynomials yago:MathematicalRelation113783581 yago:Statement106722453 yago:WikicatTheoremsInAlgebra yago:Theorem106752293 yago:Function113783816
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Théorème d'irréductibilité de Hilbert Irreduzibilitätssatz von Hilbert Hilbert's irreducibility theorem
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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. 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 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.
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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. 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. 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.
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