Theorems · Theorem · nonassociative algebras

lie_eq_self_of_isAtom_of_ne_bot

∀ {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}
  {I : LieIdeal R L}, IsAtom N → ⁅I, N⁆ ≠ ⊥ → ⁅I, N⁆ = N

Defined in

Mathlib.Algebra.Lie.Abelian

Cited by

1 results in Mathlib

Foundations

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

Assumes

CommRingLieRingLieAlgebraAddCommGroupModuleLieRingModule