Theorems · Theorem · field theory

IsGaloisGroup.algebraMap_quotientMulEquiv_smul

∀ (G : Type u_1) (G' : Type u_2) [inst : Group G] [inst_1 : Group G'] (A : Type u_5) (B : Type u_6) (C : Type u_7)
  [inst_2 : CommRing A] [inst_3 : CommRing B] [inst_4 : CommRing C] [inst_5 : IsDomain C] [inst_6 : Algebra A B]
  [inst_7 : Algebra A C] [inst_8 : Algebra B C] [inst_9 : FaithfulSMul A B] [inst_10 : FaithfulSMul B C]
  [inst_11 : IsScalarTower A B C] [inst_12 : Finite G] [inst_13 : Finite G'] (N : Subgroup G) [inst_14 : N.Normal]
  [inst_15 : MulSemiringAction G C] [inst_16 : IsGaloisGroup G A C] [inst_17 : IsGaloisGroup (↥N) B C]
  [inst_18 : MulSemiringAction G' B] [inst_19 : IsGaloisGroup G' A B] (g : G) (x : B),
  (algebraMap B C) ((IsGaloisGroup.quotientMulEquiv G G' A B C N) ↑g • x) = g • (algebraMap B C) x

Defined in

Mathlib.FieldTheory.Galois.IsGaloisGroup

Cited by

1 results in Mathlib

Foundations

Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

GroupGroupCommRingCommRingCommRingIsDomainAlgebraAlgebraAlgebraFaithfulSMulFaithfulSMulIsScalarTowerFiniteFiniteSubgroup.NormalMulSemiringActionIsGaloisGroupIsGaloisGroupMulSemiringActionIsGaloisGroup