Theorems · Theorem · nonassociative algebras

LieSubalgebra.isNilpotent_of_forall_le_engel

∀ {R : Type u_1} {L : Type u_2} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L] [IsNoetherian R L]
  (H : LieSubalgebra R L), (∀ x ∈ H, H ≤ LieSubalgebra.engel R x) → LieRing.IsNilpotent ↥H

A Lie subalgebra of a Noetherian Lie algebra is nilpotent if it is contained in the Engel subalgebra of all its elements.

Defined in

Mathlib.Algebra.Lie.EngelSubalgebra

Cited by

1 results in Mathlib

Foundations

Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraIsNoetherian