Theorems · Theorem · ring theory
Subalgebra.mem_centralizer_iff
∀ (R : Type u) {A : Type v} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A] {s : Set A} {z : A},
z ∈ Subalgebra.centralizer R s ↔ ∀ g ∈ s, g * z = z * g- Defined in
- Mathlib.Algebra.Algebra.Subalgebra.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Quot.sound
- Assumes
- CommSemiringSemiringAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Subalgebrastatement · cited by 1,353
- Subalgebra.centralizerstatement · cited by 25
Cited by1
Results whose statement or proof uses this declaration.
- Subalgebra.centralizer_coe_image_includeLeft_eq_center_tensorProductproof · cited by 2