Theorems · Definition · ring theory

NonUnitalStarSubalgebra.toStarSubalgebra

{R : Type u_1} →
  {A : Type u_2} →
    [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] → (S : NonUnitalStarSubalgebra R A) → 1 ∈ S → StarSubalgebra R A

Turn a non-unital star subalgebra containing 1 into a StarSubalgebra.

Defined in

Mathlib.Algebra.Star.Subalgebra

Cited by

2 results in Mathlib

Foundations

Depth 20 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringStarRingSemiringStarRingAlgebraStarModule