Theorems · Theorem · ring theory
StarSubalgebra.mem_centralizer_iff
∀ (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] {s : Set A} {z : A},
z ∈ StarSubalgebra.centralizer R s ↔ ∀ g ∈ s, g * z = z * g ∧ star g * z = z * star g- Defined in
- Mathlib.Algebra.Star.Subalgebra
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Quot.sound
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Cites12
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
- Set.imageproof · cited by 5,609
- StarRingstatement and proof · cited by 1,686
- Star.starstatement and proof · cited by 1,082
- StarModulestatement and proof · cited by 570
- StarSubalgebrastatement · cited by 194
- Set.centralizerproof · cited by 57
- StarSubalgebra.centralizerstatement · cited by 9
- Set.centralizer_unionproof · cited by 2
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