Theorems · Theorem · commutative algebra

IsGaloisGroup.mulEquivAlgEquiv_symm_apply

∀ (G : Type u_1) [inst : Group G] (A : Type u_2) (B : Type u_3) [inst_1 : CommRing A] [inst_2 : CommRing B]
  [inst_3 : IsDomain B] [inst_4 : Algebra A B] [inst_5 : FaithfulSMul A B] [inst_6 : MulSemiringAction G B]
  [inst_7 : IsGaloisGroup G A B] [inst_8 : Finite G] (b : B ≃ₐ[A] B),
  (IsGaloisGroup.mulEquivAlgEquiv G A B).symm b = Function.surjInv ⋯ b

Defined in

Mathlib.RingTheory.IsGaloisGroup.Basic

Cited by

0 results in Mathlib

Foundations

Depth 148 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

GroupCommRingCommRingIsDomainAlgebraFaithfulSMulMulSemiringActionIsGaloisGroupFinite