Theorems · Theorem · ring theory
NonUnitalSubalgebra.starClosure_le
∀ {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] {S₁ : NonUnitalSubalgebra R A} {S₂ : NonUnitalStarSubalgebra R A},
S₁ ≤ S₂.toNonUnitalSubalgebra → S₁.starClosure ≤ S₂- Defined in
- Mathlib.Algebra.Star.NonUnitalSubalgebra
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- CommSemiringstatement and proof · cited by 10,911
- IsScalarTowerstatement and proof · cited by 3,896
- SMulCommClassstatement and proof · cited by 1,927
- StarRingstatement and proof · cited by 1,686
- Star.starproof · cited by 1,082
- StarModulestatement and proof · cited by 570
- NonUnitalSemiringstatement and proof · cited by 339
- NonUnitalSubalgebrastatement and proof · cited by 215
- NonUnitalStarSubalgebrastatement and proof · cited by 196
- sup_leproof · cited by 159
- star_starproof · cited by 135
Cited by2
Results whose statement or proof uses this declaration.
- NonUnitalSubalgebra.starClosure_le_iffproof · cited by 1
- NonUnitalSubalgebra.starClosure_monoproof · cited by 0