Theorems · Theorem · ring theory

AlgEquiv.ofLinearEquiv_apply

∀ {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) (map_one : l 1 = 1)
  (map_mul : ∀ (x y : A₁), l (x * y) = l x * l y) (a : A₁), (AlgEquiv.ofLinearEquiv l map_one map_mul) a = l a

Defined in

Mathlib.Algebra.Algebra.Equiv

Cited by

7 results in Mathlib

Foundations

Depth 28 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringSemiringSemiringAlgebraAlgebra