Theorems · Theorem · ring theory

Unitization.starMap_surjective

∀ {R : Type u_1} {A : Type u_2} {B : Type u_3} [inst : CommSemiring R] [inst_1 : StarRing R]
  [inst_2 : NonUnitalSemiring A] [inst_3 : StarRing A] [inst_4 : Module R A] [inst_5 : SMulCommClass R A A]
  [inst_6 : IsScalarTower R A A] [inst_7 : NonUnitalSemiring B] [inst_8 : StarRing B] [inst_9 : Module R B]
  [inst_10 : SMulCommClass R B B] [inst_11 : IsScalarTower R B B] [inst_12 : StarModule R B] {φ : A →⋆ₙₐ[R] B},
  Function.Surjective ⇑φ → Function.Surjective ⇑(Unitization.starMap φ)

If φ : A →⋆ₙₐ[R] B is surjective, the lift starMap φ : Unitization R A →⋆ₐ[R] Unitization R B is also surjective.

Defined in

Mathlib.Algebra.Algebra.Unitization

Cited by

0 results in Mathlib

Foundations

Depth 40 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringStarRingNonUnitalSemiringStarRingModuleSMulCommClassIsScalarTowerNonUnitalSemiringStarRingModuleSMulCommClassIsScalarTowerStarModule