Theorems · Definition · field theory

Normal.algHomEquivAut

(F : Type u_1) →
  [inst : Field F] →
    (K₁ : Type u_3) →
      [inst_1 : Field K₁] →
        [inst_2 : Algebra F K₁] →
          (E : Type u_6) →
            [inst_3 : Field E] →
              [inst_4 : Algebra F E] →
                [inst_5 : Algebra E K₁] → [IsScalarTower F E K₁] → [Normal F E] → (E →ₐ[F] K₁) ≃ Gal(E/F)

If K₁/E/F is a tower of fields with E/F normal then AlgHom.restrictNormal' is an equivalence.

Defined in

Mathlib.FieldTheory.Normal.Defs

Cited by

5 results in Mathlib

Foundations

Depth 149 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldFieldAlgebraFieldAlgebraAlgebraIsScalarTowerNormal