Theorems · Definition · ring theory
StarSubalgebra.centralizer
(R : Type u_2) →
{A : Type u_3} →
[inst : CommSemiring R] →
[inst_1 : StarRing R] →
[inst_2 : Semiring A] →
[inst_3 : StarRing A] → [inst_4 : Algebra R A] → [inst_5 : StarModule R A] → Set A → StarSubalgebra R AThe centralizer, or commutant, of the star-closure of a set as a star subalgebra.
- Defined in
- Mathlib.Algebra.Star.Subalgebra
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- StarSubalgebrastatement · cited by 194
- Subalgebra.centralizerproof · cited by 25
Cited by10
Results whose statement or proof uses this declaration.
- VonNeumannAlgebra.commutantproof · cited by 5
- StarAlgebra.adjoin_le_centralizer_centralizerstatement and proof · cited by 2
- StarSubalgebra.centralizer_toSubalgebrastatement · cited by 1
- StarSubalgebra.coe_centralizerstatement · cited by 1
- StarSubalgebra.coe_centralizer_centralizerstatement and proof · cited by 1
- StarSubalgebra.topologicalClosure_adjoin_le_centralizer_centralizerstatement and proof · cited by 1
- StarSubalgebra.centralizer_lestatement · cited by 0
- StarSubalgebra.mem_centralizer_iffstatement · cited by 0
- StarAlgebra.isMulCommutative_adjoinproof · cited by 0
- StarAlgebra.elemental.le_centralizer_centralizerstatement · cited by 0