Theorems · Theorem · nonassociative algebras
Set.smul_mem_centralizer
∀ {R : Type u_1} {A : Type u_2} [inst : CommSemiring R] [inst_1 : NonUnitalSemiring A] [inst_2 : Module R A]
[IsScalarTower R A A] [SMulCommClass R A A] {s : Set A} (r : R) {a : A}, a ∈ s.centralizer → r • a ∈ s.centralizer- Cited by
- 0 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Modulestatement and proof · cited by 20,661
- CommSemiringstatement and proof · cited by 10,911
- IsScalarTowerstatement and proof · cited by 3,896
- SMulCommClassstatement and proof · cited by 1,927
- NonUnitalSemiringstatement and proof · cited by 339
- smul_mul_assocproof · cited by 77
- mul_smul_commproof · cited by 65
- Set.centralizerstatement and proof · cited by 57
Cited by1
Results whose statement or proof uses this declaration.
- NonUnitalSubalgebra.centralizerproof · cited by 12