Theorems · Theorem · commutative algebra

IsGaloisGroup.iff_of_mulEquiv

∀ {G : Type u_1} {A : Type u_2} {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] {H : Type u_5} [inst_5 : Group H]
  [inst_6 : MulSemiringAction H B] (e : H ≃* G),
  (∀ (h : H) (x : B), e h • x = h • x) → (IsGaloisGroup H A B ↔ IsGaloisGroup G A B)

Defined in

Mathlib.RingTheory.IsGaloisGroup.Defs

Cited by

1 results in Mathlib

Foundations

Depth 19 from the axioms · uses propext, Quot.sound

Assumes

GroupCommSemiringSemiringAlgebraMulSemiringActionGroupMulSemiringAction