Theorems · Theorem · ring theory
Subalgebra.center_le_centralizer
∀ (R : Type u) {A : Type v} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A] (s : Set A),
Subalgebra.center R A ≤ Subalgebra.centralizer R s- Defined in
- Mathlib.Algebra.Algebra.Subalgebra.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringSemiringAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Subalgebra.centerstatement · cited by 24
- Set.center_subset_centralizerproof · cited by 8
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