Theorems · Definition · ring theory

AlgEquiv.toLinearEquiv

{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 ≃ₗ[R] A₂

Forgetting the multiplicative structures, an equivalence of algebras is a linear equivalence.

Defined in

Mathlib.Algebra.Algebra.Equiv

Cited by

117 results in Mathlib

Foundations

Depth 23 from the axioms, rests on 247 definitions · uses propext, Quot.sound

Assumes

CommSemiringSemiringSemiringAlgebraAlgebra