Theorems · Inductive type · ring theory
Algebra.IsCentral
(K : Type u) → [inst : CommSemiring K] → (D : Type v) → [inst_1 : Semiring D] → [Algebra K D] → Prop
For a commutative ring K and a K-algebra D, we say that D is a central algebra over K if
the center of D is the image of K in D.
- Defined in
- Mathlib.Algebra.Central.Defs
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
- Assumes
- CommSemiringSemiringAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement · cited by 13,802
- Algebrastatement · cited by 11,388
- CommSemiringstatement · cited by 10,911
Cited by24
Results whose statement or proof uses this declaration.
- Algebra.IsCentral.center_eq_botstatement and proof · cited by 8
- Algebra.IsCentral.outstatement and proof · cited by 4
- Algebra.IsCentral.left_of_tensorstatement and proof · cited by 2
- Algebra.IsCentral.of_algEquivstatement and proof · cited by 1
- Algebra.IsCentral.right_of_tensorstatement and proof · cited by 1
- LinearEquiv.conjAlgEquiv_ext_iffstatement and proof · cited by 1
- CSA.mk.injstatement and proof · cited by 1
- CSA.mk.noConfusionstatement and proof · cited by 1
- CSA.noConfusionproof · cited by 0
- CSA.recOnstatement and proof · cited by 0
- Algebra.IsCentral.recOnstatement and proof · cited by 0
- Algebra.IsCentral.right_of_tensor_of_fieldstatement and proof · cited by 0