Theorems · Definition · ring theory
Subalgebra.center
(R : Type u) → (A : Type v) → [inst : CommSemiring R] → [inst_1 : Semiring A] → [inst_2 : Algebra R A] → Subalgebra R A
The center of an algebra is the set of elements which commute with every element. They form a subalgebra.
- Defined in
- Mathlib.Algebra.Algebra.Subalgebra.Basic
- Cited by
- 24 results in Mathlib
- Foundations
- Depth 22 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- 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
- Subsemiringproof · cited by 456
- Subsemiring.centerproof · cited by 18
- Set.algebraMap_mem_centerproof · cited by 0
Cited by26
Results whose statement or proof uses this declaration.
- Algebra.IsCentral.center_eq_botstatement · cited by 8
- Subalgebra.mem_center_iffstatement · cited by 6
- Algebra.IsCentral.outstatement · cited by 4
- Subalgebra.centralizer_univstatement · cited by 2
- Algebra.IsCentral.of_algEquivproof · cited by 1
- Subalgebra.center_toSubringstatement · cited by 1
- Subalgebra.centralizer_coe_range_includeLeft_eq_center_tensorProductstatement · cited by 1
- Subalgebra.centralizer_range_includeRight_eq_center_tensorProductstatement · cited by 1
- Algebra.TensorProduct.includeLeft_map_center_lestatement and proof · cited by 1
- Algebra.IsCentral.recOnstatement and proof · cited by 0
- Subalgebra.center_eq_topstatement and proof · cited by 0
- Subalgebra.center_le_centralizerstatement · cited by 0