Theorems · Theorem · ring theory
StarAlgebra.adjoin_eq_span
∀ {R : Type u_2} {A : Type u_3} [inst : CommSemiring R] [inst_1 : StarRing R] [inst_2 : Semiring A]
[inst_3 : Algebra R A] [inst_4 : StarRing A] [inst_5 : StarModule R A] (s : Set A),
Subalgebra.toSubmodule (StarAlgebra.adjoin R s).toSubalgebra = Submodule.span R ↑(Submonoid.closure (s ∪ star s))- Defined in
- Mathlib.Algebra.Star.Subalgebra
- Cited by
- 1 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.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- SetLike.coestatement and proof · cited by 8,199
- Submodulestatement and proof · cited by 7,192
- Submonoidstatement · cited by 3,086
- StarRingstatement and proof · cited by 1,686
- Submodule.spanstatement and proof · cited by 1,504
- Subalgebrastatement and proof · cited by 1,353
- Star.starstatement and proof · cited by 1,082
Cited by1
Results whose statement or proof uses this declaration.
- StarAlgebra.adjoin_nonUnitalStarSubalgebra_eq_spanproof · cited by 2