Theorems · Theorem · ring theory

Unitization.starMap_apply

∀ {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)
  (x : Unitization R A), (Unitization.starMap φ) x = (algebraMap R (Unitization R B)) x.toProd.1 + ↑(φ x.toProd.2)

Defined in

Mathlib.Algebra.Algebra.Unitization

Cited by

3 results in Mathlib

Foundations

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

Assumes

CommSemiringStarRingNonUnitalSemiringStarRingModuleSMulCommClassIsScalarTowerNonUnitalSemiringStarRingModuleSMulCommClassIsScalarTowerStarModule