Theorems · Theorem · nonassociative algebras

LieModule.map_lowerCentralSeries_le

∀ {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) {M₂ : Type w₁}
  [inst_6 : AddCommGroup M₂] [inst_7 : Module R M₂] [inst_8 : LieRingModule L M₂] [LieModule R L M₂] [LieModule R L M]
  (f : M →ₗ⁅R,L⁆ M₂), LieSubmodule.map f (LieModule.lowerCentralSeries R L M k) ≤ LieModule.lowerCentralSeries R L M₂ k

Defined in

Mathlib.Algebra.Lie.Nilpotent

Cited by

2 results in Mathlib

Foundations

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

Assumes

CommRingLieRingLieAlgebraAddCommGroupModuleLieRingModuleAddCommGroupModuleLieRingModuleLieModuleLieModule