Theorems · Definition · ring theory

AlgHom.ofLinearMap

{R : Type u} →
  {A : Type v} →
    {B : Type w} →
      [inst : CommSemiring R] →
        [inst_1 : Semiring A] →
          [inst_2 : Semiring B] →
            [inst_3 : Algebra R A] →
              [inst_4 : Algebra R B] → (f : A →ₗ[R] B) → f 1 = 1 → (∀ (x y : A), f (x * y) = f x * f y) → A →ₐ[R] B

Promote a LinearMap to an AlgHom by supplying proofs about the behavior on 1 and *.

Defined in

Mathlib.Algebra.Algebra.Hom

Cited by

11 results in Mathlib

Foundations

Depth 25 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringSemiringSemiringAlgebraAlgebra