Theorems · Theorem · ring theory
NonUnitalSubalgebra.star_adjoin_comm
∀ (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] [inst_5 : StarModule R A] [inst_6 : IsScalarTower R A A]
[inst_7 : SMulCommClass R A A] (s : Set A), star (NonUnitalAlgebra.adjoin R s) = NonUnitalAlgebra.adjoin R (star s)The star operation on NonUnitalSubalgebra commutes with NonUnitalAlgebra.adjoin.
- Defined in
- Mathlib.Algebra.Star.NonUnitalSubalgebra
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Modulestatement and proof · cited by 20,661
- CommSemiringstatement and proof · cited by 10,911
- IsScalarTowerstatement and proof · cited by 3,896
- le_antisymmproof · cited by 2,068
- SMulCommClassstatement and proof · cited by 1,927
- StarRingstatement and proof · cited by 1,686
- Star.starstatement and proof · cited by 1,082
- StarModulestatement and proof · cited by 570
- NonUnitalSemiringstatement and proof · cited by 339
- NonUnitalSubalgebrastatement · cited by 215
- star_starproof · cited by 135
Cited by1
Results whose statement or proof uses this declaration.
- NonUnitalStarAlgebra.adjoin_eq_starClosure_adjoinproof · cited by 0