Theorems · Theorem · field theory

IsGaloisGroup.fixedPoints_eq_range_algebraMap

∀ (G : Type u_1) (K : Type u_3) (L : Type u_4) [inst : Group G] [inst_1 : Field K] [inst_2 : Field L]
  [inst_3 : Algebra K L] [inst_4 : MulSemiringAction G L] (H : Subgroup G) [hGKL : IsGaloisGroup G K L] (B : Type u_5)
  [inst_5 : CommSemiring B] [inst_6 : Algebra B L] [IsGaloisGroup (↥H) B L],
  ↑(FixedPoints.intermediateField ↥H) = Set.range ⇑(algebraMap B L)

If G acts as a Galois group on L/K and the subgroup H acts as a Galois group on L/B, then the fixed points of H equals the range of algebraMap B L.

Defined in

Mathlib.FieldTheory.Galois.IsGaloisGroup

Cited by

1 results in Mathlib

Foundations

Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

GroupFieldFieldAlgebraMulSemiringActionIsGaloisGroupCommSemiringAlgebraIsGaloisGroup