Theorems · Definition · ring theory

AlgEquiv.autCongr

{R : Type uR} →
  {A₁ : Type uA₁} →
    {A₂ : Type uA₂} →
      [inst : CommSemiring R] →
        [inst_1 : Semiring A₁] →
          [inst_2 : Semiring A₂] →
            [inst_3 : Algebra R A₁] → [inst_4 : Algebra R A₂] → (A₁ ≃ₐ[R] A₂) → (A₁ ≃ₐ[R] A₁) ≃* A₂ ≃ₐ[R] A₂

An algebra isomorphism induces a group isomorphism between automorphism groups. This is a more bundled version of AlgEquiv.equivCongr.

Defined in

Mathlib.Algebra.Algebra.Equiv

Cited by

5 results in Mathlib

Foundations

Depth 29 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringSemiringSemiringAlgebraAlgebra