Theorems · Theorem · commutative algebra

IsGaloisGroup.algebraMap_smulOfNormal

∀ (G : Type u_1) [inst : Group G] (B : Type u_3) (C : Type u_4) [inst_1 : Semiring C] [inst_2 : MulSemiringAction G C]
  (N : Subgroup G) [inst_3 : CommSemiring B] [inst_4 : Algebra B C] [inst_5 : N.Normal]
  [inst_6 : IsGaloisGroup (↥N) B C] (g : G) (x : B), (algebraMap B C) (g • x) = g • (algebraMap B C) x

Defined in

Mathlib.RingTheory.IsGaloisGroup.Basic

Cited by

2 results in Mathlib

Foundations

Depth 26 from the axioms · uses propext, Classical.choice

Assumes

GroupSemiringMulSemiringActionCommSemiringAlgebraSubgroup.NormalIsGaloisGroup