Theorems · Theorem · nonassociative algebras
LieAlgebra.ad_nilpotent_of_nilpotent
∀ {R : Type u_1} {A : Type u_2} [inst : CommRing R] [inst_1 : Ring A] [inst_2 : Algebra R A] {a : A},
IsNilpotent a → IsNilpotent ((LieAlgebra.ad R A) a)The adjoint of a nilpotent element is nilpotent.
- Defined in
- Mathlib.Algebra.Lie.AdjointAction.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Module.Endstatement and proof · cited by 774
- LieHomstatement · cited by 382
- IsNilpotentstatement and proof · cited by 248
- LieRing.ofAssociativeRingstatement · cited by 227
- LieAlgebra.adstatement · cited by 49
- LinearMap.mulLeftproof · cited by 34
- LinearMap.mulRightproof · cited by 24
Cited by2
Results whose statement or proof uses this declaration.
- LieAlgebra.isNilpotent_ad_of_isNilpotentproof · cited by 1
- LieAlgebra.ad_mem_adjoin_of_isSemisimpleproof · cited by 1