Theorems · Definition · ring theory

AlgEquiv.ofLinearEquiv

{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] →
                (l : A₁ ≃ₗ[R] A₂) → l 1 = 1 → (∀ (x y : A₁), l (x * y) = l x * l y) → A₁ ≃ₐ[R] A₂

Upgrade a linear equivalence to an algebra equivalence, given that it distributes over multiplication and the identity

Defined in

Mathlib.Algebra.Algebra.Equiv

Cited by

7 results in Mathlib

Foundations

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

Assumes

CommSemiringSemiringSemiringAlgebraAlgebra