Theorems · Theorem · ring theory
NonUnitalStarAlgebra.subset_adjoin
∀ (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 : IsScalarTower R A A] [inst_6 : SMulCommClass R A A]
[inst_7 : StarModule R A] (s : Set A), s ⊆ ↑(NonUnitalStarAlgebra.adjoin R s)- Defined in
- Mathlib.Algebra.Star.NonUnitalSubalgebra
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- SetLike.coestatement · cited by 8,199
- IsScalarTowerstatement and proof · cited by 3,896
- LE.le.transproof · cited by 3,151
- SMulCommClassstatement and proof · cited by 1,927
- StarRingstatement and proof · cited by 1,686
- StarModulestatement and proof · cited by 570
- NonUnitalSemiringstatement and proof · cited by 339
- NonUnitalStarSubalgebrastatement · cited by 196
- Set.subset_union_leftproof · cited by 142
Cited by5
Results whose statement or proof uses this declaration.
- StarAlgebra.adjoin_nonUnitalStarSubalgebraproof · cited by 2
- NonUnitalStarAlgebra.adjoin_eqproof · cited by 1
- NonUnitalStarAlgebra.adjoin_inductionstatement and proof · cited by 1
- NonUnitalStarAlgebra.mem_adjoin_of_memproof · cited by 0
- NonUnitalSubalgebra.starClosure_eq_adjoinproof · cited by 0