Theorems · Theorem · commutative algebra

IsGaloisGroup.of_ringHom_surjective

∀ (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] [hG : IsGaloisGroup G A B]
  [inst_5 : CommSemiring A'] [inst_6 : Algebra A' B] (e : A →+* A'),
  (∀ (a : A), (algebraMap A' B) (e a) = (algebraMap A B) a) → Function.Surjective ⇑e → IsGaloisGroup G A' B

Defined in

Mathlib.RingTheory.IsGaloisGroup.Defs

Cited by

1 results in Mathlib

Foundations

Depth 18 from the axioms · uses no axioms

Assumes

GroupCommSemiringSemiringAlgebraMulSemiringActionIsGaloisGroupCommSemiringAlgebra