Theorems · Definition · ring theory

AlgEquiv.ofBijective

{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] → (f : A₁ →ₐ[R] A₂) → Function.Bijective ⇑f → A₁ ≃ₐ[R] A₂

Promotes a bijective algebra homomorphism to an algebra equivalence.

Defined in

Mathlib.Algebra.Algebra.Equiv

Cited by

34 results in Mathlib

Foundations

Depth 24 from the axioms · uses Classical.choice

Assumes

CommSemiringSemiringSemiringAlgebraAlgebra