Theorems · Theorem · ring theory

AlgHom.commutes

∀ {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] (φ : A →ₐ[R] B) (r : R), φ ((algebraMap R A) r) = (algebraMap R B) r

Defined in

Mathlib.Algebra.Algebra.Hom

Cited by

96 results in Mathlib

Foundations

Depth 21 from the axioms, rests on 127 definitions · uses no axioms

Assumes

CommSemiringSemiringSemiringAlgebraAlgebra