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Theorems · Theorem · field theory

IsGalois.of_separable_splitting_field

∀ {F : Type u_1} [inst : Field F] {E : Type u_2} [inst_1 : Field E] [inst_2 : Algebra F E] {p : Polynomial F}
  [Polynomial.IsSplittingField F E p], p.Separable → IsGalois F E
Defined in
Mathlib.FieldTheory.Galois.Basic
Cited by
3 results in Mathlib
Foundations
Depth 197 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FieldFieldAlgebraPolynomial.IsSplittingField
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

isGalois_of_isSplittingField_X_pow_sub_C · cited by 2isGalois_of_isSplittingFi…IsGalois.tfae · cited by 2IsGalois.tfaeIsGalois.sup_right · cited by 0IsGalois.sup_rightAlgebra · cited by 11388AlgebraField · cited by 7404FieldPolynomial · cited by 5681PolynomialIsGalois · cited by 149IsGaloisPolynomial.Separable · cited by 117Polynomial.SeparablePolynomial.IsSplittingField · cited by 50Polynomial.IsSplittingFie…IsGalois.of_separable_splitti…CITED BYCITES

Cites6

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Cited by3

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