Theorems · Definition · ring theory

NonUnitalStarSubalgebra.unitization

{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] →
                [StarModule R A] →
                  [inst_6 : SetLike S A] →
                    [hSA : NonUnitalSubsemiringClass S A] →
                      [hSRA : SMulMemClass S R A] → [inst_7 : StarMemClass S A] → (s : S) → Unitization R ↥s →⋆ₐ[R] A

The natural star R-algebra homomorphism from the unitization of a non-unital star subalgebra to its StarAlgebra.adjoin.

Defined in

Mathlib.Algebra.Algebra.Subalgebra.Unitization

Cited by

4 results in Mathlib

Foundations

Depth 39 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringStarRingSemiringStarRingAlgebraStarModuleSetLikeNonUnitalSubsemiringClassSMulMemClassStarMemClass