Theorems · Theorem · ring theory
StarAlgebra.adjoin_nonUnitalStarSubalgebra_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 : NonUnitalStarSubalgebra R A),
Subalgebra.toSubmodule (StarAlgebra.adjoin R ↑s).toSubalgebra = R ∙ 1 ⊔ s.toSubmodule- Defined in
- Mathlib.Algebra.Star.Subalgebra
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites25
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · 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
- StarRingstatement and proof · cited by 1,686
- Submodule.spanstatement and proof · cited by 1,504
- Subalgebrastatement · cited by 1,353
- Star.starproof · cited by 1,082
- OrderEmbeddingstatement · cited by 619
Cited by2
Results whose statement or proof uses this declaration.
- ContinuousMap.adjoin_id_eq_span_one_addproof · cited by 1
- ContinuousMap.adjoin_id_eq_span_one_unionproof · cited by 0