Theorems · Theorem · ring theory

NonUnitalStarSubalgebra.unitization_apply

∀ {R : Type u_1} {S : Type u_2} {A : Type u_3} [inst : CommSemiring R] [inst_1 : StarRing R] [inst_2 : Semiring A]
  [inst_3 : StarRing A] [inst_4 : Algebra R A] [inst_5 : StarModule R A] [inst_6 : SetLike S A]
  [hSA : NonUnitalSubsemiringClass S A] [hSRA : SMulMemClass S R A] [inst_7 : StarMemClass S A] (s : S)
  (x : Unitization R ↥s), (NonUnitalStarSubalgebra.unitization s) x = (algebraMap R A) x.toProd.1 + ↑x.toProd.2

Defined in

Mathlib.Algebra.Algebra.Subalgebra.Unitization

Cited by

0 results in Mathlib

Foundations

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

Assumes

CommSemiringStarRingSemiringStarRingAlgebraStarModuleSetLikeNonUnitalSubsemiringClassSMulMemClassStarMemClass