Theorems · Theorem · nonassociative algebras

LieModule.nilpotencyLength_eq_succ_iff

∀ (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] [LieModule R L M] (k : ℕ),
  LieModule.nilpotencyLength L M = k + 1 ↔
    LieModule.lowerCentralSeries R L M (k + 1) = ⊥ ∧ LieModule.lowerCentralSeries R L M k ≠ ⊥

Defined in

Mathlib.Algebra.Lie.Nilpotent

Cited by

3 results in Mathlib

Foundations

Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraAddCommGroupModuleLieRingModuleLieModule