Theorems · Theorem · nonassociative algebras

LieAlgebra.isEngelian_of_isNoetherian

∀ {R : Type u₁} {L : Type u₂} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L] [IsNoetherian R L],
  LieAlgebra.IsEngelian R L

Engel's theorem. Note that this implies all traditional forms of Engel's theorem via LieModule.nontrivial_max_triv_of_isNilpotent, LieModule.isNilpotent_iff_forall, LieAlgebra.isNilpotent_iff_forall.

Defined in

Mathlib.Algebra.Lie.Engel

Cited by

1 results in Mathlib

Foundations

Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraIsNoetherian