Theorems · Theorem · nonassociative algebras

LieSubmodule.lowerCentralSeries_eq_bot_iff_lcs_eq_bot

∀ {R : Type u} {L : Type v} {M : Type w} [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] (k : ℕ) (N : LieSubmodule R L M)
  [LieModule R L M], LieModule.lowerCentralSeries R L (↥N) k = ⊥ ↔ LieSubmodule.lcs k N = ⊥

Defined in

Mathlib.Algebra.Lie.Nilpotent

Cited by

0 results in Mathlib

Foundations

Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraAddCommGroupModuleLieRingModuleLieModule