“GaloisCriterionForSolvabilityOfAPolynomialByRadicals”的概念、定义、习题解题方法及翻译-数学辞典

单词	GaloisCriterionForSolvabilityOfAPolynomialByRadicals
释义	Galois criterion for solvability of a polynomial by radicals Let $f\\in F[x]$ be a polynomial over a field $F$ , and let $K$ be its splitting field. If $K$ is a radical extension of $F$ , then the Galois group $\\operatorname{Gal}(K/F)$ is a solvable group. Conversely, if the Galois group $\\operatorname{Gal}(K/F)$ is a solvable group, then $K$ is a radical extension of $F$ provided that the characteristic of $K$ is either $0$ or greater than $\\deg(f)$ .
随便看	proof of Riemann-Roch theorem ProofOfRiemannsRemovableSingularityTheorem proof of Riemann’s removable singularity theorem ProofOfRieszLemma ProofOfRieszRepresentationTheorem proof of Riesz representation theorem ProofOfRieszRepresentationTheoremForSeparableHilbertSpaces proof of Riesz representation theorem for separable Hilbert spaces proof of Riesz’ Lemma ProofOfRodriguesRotationFormula proof of Rodrigues’ rotation formula ProofOfRollesTheorem proof of Rolle’s theorem ProofOfRouchesTheorem proof of Rouché’s theorem ProofOfRuffasFormulaForContinuousFunctions proof of Ruffa’s formula for continuous functions ProofOfSamplingTheorem proof of sampling theorem ProofOfSchauderFixedPointTheorem proof of Schauder fixed point theorem ProofOfSchroederBernsteinTheoremUsingTarskiKnasterTheorem proof of Schroeder-Bernstein theorem using Tarski-Knaster theorem ProofOfSchursInequality proof of Schur’s inequality

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Galois criterion for solvability of a polynomial by radicals