Theorems · Theorem · ring theory
LinearMap.commute_mulLeft_right
∀ {R : Type u_1} {A : Type u_2} [inst : CommSemiring R] [inst_1 : NonUnitalSemiring A] [inst_2 : Module R A]
[inst_3 : SMulCommClass R A A] [inst_4 : IsScalarTower R A A] (a b : A),
Commute (LinearMap.mulLeft R a) (LinearMap.mulRight R b)- Defined in
- Mathlib.Algebra.Algebra.Bilinear
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement · cited by 10,215
- IsScalarTowerstatement and proof · cited by 3,896
- SMulCommClassstatement and proof · cited by 1,927
- mul_assocproof · cited by 1,667
- LinearMap.extproof · cited by 844
- Commutestatement · cited by 639
- NonUnitalSemiringstatement and proof · cited by 339
- LinearMap.mulLeftstatement · cited by 34
- LinearMap.mulRightstatement · cited by 24
Cited by3
Results whose statement or proof uses this declaration.
- LieAlgebra.ad_nilpotent_of_nilpotentproof · cited by 2
- JacobsonNoether.exist_pow_eq_zero_of_leproof · cited by 1
- LieAlgebra.ad_isSemisimple_of_isSemisimpleproof · cited by 1