Theorems · Definition · ring theory

AlgHom.fromOpposite

{R : Type u_1} →
  {A : Type u_3} →
    {B : Type u_4} →
      [inst : CommSemiring R] →
        [inst_1 : Semiring A] →
          [inst_2 : Semiring B] →
            [inst_3 : Algebra R A] →
              [inst_4 : Algebra R B] → (f : A →ₐ[R] B) → (∀ (x y : A), Commute (f x) (f y)) → Aᵐᵒᵖ →ₐ[R] B

An algebra homomorphism f : A →ₐ[R] B such that f x commutes with f y for all x, y defines an algebra homomorphism from Aᵐᵒᵖ.

Defined in

Mathlib.Algebra.Algebra.Opposite

Cited by

3 results in Mathlib

Foundations

Depth 29 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringSemiringSemiringAlgebraAlgebra