Theorems · Theorem · ring theory
StarAlgebra.adjoin_toSubalgebra
∀ (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),
(StarAlgebra.adjoin R s).toSubalgebra = Algebra.adjoin R (s ∪ star s)- Defined in
- Mathlib.Algebra.Star.Subalgebra
- Cited by
- 4 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.
Cites11
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
- Subalgebrastatement · cited by 1,353
- Star.starstatement · cited by 1,082
- StarModulestatement and proof · cited by 570
- Algebra.adjoinstatement · cited by 535
- StarSubalgebra.toSubalgebrastatement · cited by 58
- StarAlgebra.adjoinstatement · cited by 42
Cited by4
Results whose statement or proof uses this declaration.
- StarAlgebra.gcproof · cited by 4
- StarAlgebra.adjoin_le_centralizer_centralizerproof · cited by 2
- StarAlgebra.adjoin_eq_spanproof · cited by 1
- StarAlgebra.elemental.induction_onproof · cited by 0