Theorems · Theorem · ring theory

NonUnitalAlgHom.toAlgHom_apply

∀ {R : Type u_2} {A : Type u_3} [inst : CommSemiring R] [inst_1 : NonUnitalSemiring A] [inst_2 : Module R A]
  [inst_3 : SMulCommClass R A A] [inst_4 : IsScalarTower R A A] {C : Type u_5} [inst_5 : Semiring C]
  [inst_6 : Algebra R C] (φ : A →ₙₐ[R] C) (x : Unitization R A),
  φ.toAlgHom x = (algebraMap R C) x.toProd.1 + φ x.toProd.2

Defined in

Mathlib.Algebra.Algebra.Unitization

Cited by

4 results in Mathlib

Foundations

Depth 32 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringNonUnitalSemiringModuleSMulCommClassIsScalarTowerSemiringAlgebra