Theorems · Theorem · ring theory
NonUnitalStarAlgebra.adjoin_eq_span
∀ {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),
(NonUnitalStarAlgebra.adjoin R s).toSubmodule = Submodule.span R ↑(Subsemigroup.closure (s ∪ star s))- Defined in
- Mathlib.Algebra.Star.NonUnitalSubalgebra
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
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 and proof · cited by 8,199
- Submodulestatement and proof · cited by 7,192
- IsScalarTowerstatement and proof · cited by 3,896
- SMulCommClassstatement and proof · cited by 1,927
- StarRingstatement and proof · cited by 1,686
- Submodule.spanstatement and proof · cited by 1,504
- Star.starstatement and proof · cited by 1,082
- StarModulestatement and proof · cited by 570
- NonUnitalSemiringstatement and proof · cited by 339
Cited by1
Results whose statement or proof uses this declaration.
- StarAlgebra.adjoin_nonUnitalStarSubalgebra_eq_spanproof · cited by 2