Theorems · Definition · ring theory

AlgEquiv.symm

{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) → A₂ ≃ₐ[R] A₁

Algebra equivalences are symmetric.

Defined in

Mathlib.Algebra.Algebra.Equiv

Cited by

615 results in Mathlib

Foundations

Depth 24 from the axioms, rests on 187 definitions · uses propext, Quot.sound

Assumes

CommSemiringSemiringSemiringAlgebraAlgebra