Theorems · Theorem · nonassociative algebras

LieSubmodule.isNilpotent_iff_exists_self_le_ucs

∀ {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] (N : LieSubmodule R L M)
  [inst_6 : LieModule R L M], LieModule.IsNilpotent L ↥N ↔ ∃ k, N ≤ LieSubmodule.ucs k ⊥

Defined in

Mathlib.Algebra.Lie.Nilpotent

Cited by

3 results in Mathlib

Foundations

Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraAddCommGroupModuleLieRingModuleLieModule