Theorems · Theorem · commutative algebra

IsGaloisGroup.algebraMap_ringEquiv_symm_apply

∀ (G : Type u_1) (A : Type u_2) (A' : Type u_3) (B : Type u_4) [inst : Group G] [inst_1 : CommSemiring A]
  [inst_2 : Semiring B] [inst_3 : Algebra A B] [inst_4 : MulSemiringAction G B] [hA : IsGaloisGroup G A B]
  [inst_5 : FaithfulSMul A B] [inst_6 : CommSemiring A'] [inst_7 : Algebra A' B] [inst_8 : FaithfulSMul A' B]
  [hA' : IsGaloisGroup G A' B] (x : A'),
  (algebraMap A B) ((IsGaloisGroup.ringEquiv G A A' B).symm x) = (algebraMap A' B) x

Defined in

Mathlib.RingTheory.IsGaloisGroup.Defs

Cited by

0 results in Mathlib

Foundations

Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

GroupCommSemiringSemiringAlgebraMulSemiringActionIsGaloisGroupFaithfulSMulCommSemiringAlgebraFaithfulSMulIsGaloisGroup