Theorems · Definition · ring theory

NonUnitalSubalgebra.starClosure

{R : Type u} →
  {A : Type v} →
    [inst : CommSemiring R] →
      [inst_1 : StarRing R] →
        [inst_2 : NonUnitalSemiring A] →
          [inst_3 : StarRing A] →
            [inst_4 : Module R A] →
              [StarModule R A] →
                [IsScalarTower R A A] → [SMulCommClass R A A] → NonUnitalSubalgebra R A → NonUnitalStarSubalgebra R A

The NonUnitalStarSubalgebra obtained from S : NonUnitalSubalgebra R A by taking the smallest non-unital subalgebra containing both S and star S.

Defined in

Mathlib.Algebra.Star.NonUnitalSubalgebra

Cited by

8 results in Mathlib

Foundations

Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringStarRingNonUnitalSemiringStarRingModuleStarModuleIsScalarTowerSMulCommClass