Theorems · Theorem · ring theory
Subalgebra.mem_center_iff
∀ {R : Type u} {A : Type v} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A] {a : A},
a ∈ Subalgebra.center R A ↔ ∀ (b : A), b * a = a * b- Defined in
- Mathlib.Algebra.Algebra.Subalgebra.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 23 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.
Cites6
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
- Subalgebra.centerstatement · cited by 24
- Subsemigroup.mem_center_iffproof · cited by 6
Cited by6
Results whose statement or proof uses this declaration.
- LinearEquiv.conjAlgEquiv_ext_iffproof · cited by 1
- Unitary.conjStarAlgAut_ext_iffproof · cited by 0
- Unitary.conjStarAlgAut_ext_iff'proof · cited by 0
- StarAlgEquiv.eq_linearIsometryEquivConjStarAlgEquivproof · cited by 0
- ContinuousLinearEquiv.conjContinuousAlgEquiv_ext_iffproof · cited by 0
- LinearIsometryEquiv.conjStarAlgEquiv_ext_iffproof · cited by 0