Theorems · Theorem · nonassociative algebras
LieAlgebra.isNilpotent_ad_of_isNilpotent
∀ {R : Type u_1} {A : Type u_2} [inst : CommRing R] [inst_1 : Ring A] [inst_2 : Algebra R A] {L : LieSubalgebra R A}
{x : ↥L}, IsNilpotent ↑x → IsNilpotent ((LieAlgebra.ad R ↥L) x)- Defined in
- Mathlib.Algebra.Lie.AdjointAction.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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 · cited by 774
- LieSubalgebrastatement and proof · cited by 418
- LieHomstatement · cited by 382
- IsNilpotentstatement and proof · cited by 248
- LieRing.ofAssociativeRingstatement · cited by 227
- LieAlgebra.adstatement · cited by 49
- LieSubalgebra.isNilpotent_ad_of_isNilpotent_adproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- LieAlgebra.isEngelian_of_isNoetherianproof · cited by 1