Theorems · Theorem · nonassociative algebras

LieModule.mem_posFittingCompOf

∀ (R : Type u_2) {L : Type u_3} {M : Type u_4} [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] [inst_6 : LieModule R L M]
  [inst_7 : LieRing.IsNilpotent L] (x : L) (m : M),
  m ∈ LieModule.posFittingCompOf R M x ↔ ∀ (k : ℕ), ∃ n, ((LieModule.toEnd R L M) x ^ k) n = m

Defined in

Mathlib.Algebra.Lie.Weights.Basic

Cited by

2 results in Mathlib

Foundations

Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraAddCommGroupModuleLieRingModuleLieModuleLieRing.IsNilpotent