Theorems · Definition · ring theory
StarAlgebra.adjoin
(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] → Set A → StarSubalgebra R AThe minimal star subalgebra that contains s.
- Defined in
- Mathlib.Algebra.Star.Subalgebra
- Cited by
- 42 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
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- StarRingstatement and proof · cited by 1,686
- Subalgebraproof · cited by 1,353
- Star.starproof · cited by 1,082
- StarModulestatement and proof · cited by 570
- Algebra.adjoinproof · cited by 535
- StarSubalgebrastatement · cited by 194
- Subsemigroup.carrierproof · cited by 160
- Submonoid.toSubsemigroupproof · cited by 159
Cited by47
Results whose statement or proof uses this declaration.
- StarAlgebra.elementalproof · cited by 26
- StarAlgebra.subset_adjoinstatement · cited by 10
- StarAlgebra.elemental.self_memproof · cited by 7
- StarAlgebra.adjoin_lestatement · cited by 5
- StarAlgebra.adjoin_toSubalgebrastatement · cited by 4
- StarAlgebra.gcstatement · cited by 4
- polynomialFunctions.starClosure_eq_adjoin_Xstatement and proof · cited by 4
- StarAlgebra.self_mem_adjoin_singletonstatement · cited by 3
- StarAlgHom.adjoin_le_equalizerstatement · cited by 2
- ContinuousMap.elemental_id_eq_topproof · cited by 2
- StarAlgHom.map_adjoinstatement · cited by 2
- NonUnitalStarAlgebra.adjoin_le_starAlgebra_adjoinstatement · cited by 2