Theorems · Theorem · ring theory

AlgHom.ofLinearMap_apply

∀ {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) (map_one : f 1 = 1)
  (map_mul : ∀ (x y : A), f (x * y) = f x * f y) (a : A), (AlgHom.ofLinearMap f map_one map_mul) a = f a

Defined in

Mathlib.Algebra.Algebra.Hom

Cited by

10 results in Mathlib

Foundations

Depth 26 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringSemiringSemiringAlgebraAlgebra