Theorems · Definition · ring theory

NonUnitalSubalgebra.toNonUnitalStarSubalgebra

{R : Type u} →
  {A : Type v} →
    [inst : CommSemiring R] →
      [inst_1 : NonUnitalSemiring A] →
        [inst_2 : Module R A] →
          [inst_3 : Star A] → (s : NonUnitalSubalgebra R A) → (∀ x ∈ s, star x ∈ s) → NonUnitalStarSubalgebra R A

A non-unital subalgebra closed under star is a non-unital star subalgebra.

Defined in

Mathlib.Algebra.Star.NonUnitalSubalgebra

Cited by

4 results in Mathlib

Foundations

Depth 15 from the axioms · uses no axioms

Assumes

CommSemiringNonUnitalSemiringModuleStar