Theorems · Theorem · nonassociative algebras

LieSubmodule.lcs_le_lcs_of_is_nilpotent_span_sup_eq_top

∀ {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]
  {I : LieIdeal R L} {x : L},
  R ∙ x ⊔ (LieIdeal.toLieSubalgebra R L I).toSubmodule = ⊤ →
    ∀ {n i j : ℕ},
      (LieModule.toEnd R L M) x ^ n = 0 →
        LieModule.lowerCentralSeries R L M i ≤ I.lcs M j → LieModule.lowerCentralSeries R L M (i + n) ≤ I.lcs M (j + 1)

Defined in

Mathlib.Algebra.Lie.Engel

Cited by

1 results in Mathlib

Foundations

Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraAddCommGroupModuleLieRingModuleLieModule