Theorems · Definition · commutative algebra

IsGaloisGroup.ringEquiv

(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] →
                    [FaithfulSMul A B] →
                      [inst_6 : CommSemiring A'] →
                        [inst_7 : Algebra A' B] → [FaithfulSMul A' B] → [hA' : IsGaloisGroup G A' B] → A ≃+* A'

If B/A and B/A' are Galois with the same Galois group, then A ≃+* A'.

Defined in

Mathlib.RingTheory.IsGaloisGroup.Defs

Cited by

2 results in Mathlib

Foundations

Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

GroupCommSemiringSemiringAlgebraMulSemiringActionIsGaloisGroupFaithfulSMulCommSemiringAlgebraFaithfulSMulIsGaloisGroup