Theorems · Theorem · nonassociative algebras

LieModule.isNilpotent_iff_forall

∀ {R : Type u₁} {L : Type u₂} {M : Type u₄} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L]
  [inst_3 : AddCommGroup M] [inst_4 : Module R M] [inst_5 : LieRingModule L M] [inst_6 : LieModule R L M]
  [IsNoetherian R L], LieModule.IsNilpotent L M ↔ ∀ (x : L), IsNilpotent ((LieModule.toEnd R L M) x)

Engel's theorem. See also LieModule.isNilpotent_iff_forall' which assumes that M is Noetherian instead of L.

Defined in

Mathlib.Algebra.Lie.Engel

Cited by

2 results in Mathlib

Foundations

Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraAddCommGroupModuleLieRingModuleLieModuleIsNoetherian