Theorems · Theorem · nonassociative algebras

LieModule.isNilpotent_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],
  LieModule.IsNilpotent L M ↔ ∃ k, LieModule.lowerCentralSeries R L M k = ⊥

See also LieModule.isNilpotent_iff_exists_ucs_eq_top.

Defined in

Mathlib.Algebra.Lie.Nilpotent

Cited by

13 results in Mathlib

Foundations

Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraAddCommGroupModuleLieRingModuleLieModule