Theorems · Theorem · nonassociative algebras

LieModule.mem_maxTrivSubmodule

∀ (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] [inst_6 : LieModule R L M] (m : M),
  m ∈ LieModule.maxTrivSubmodule R L M ↔ ∀ (x : L), ⁅x, m⁆ = 0

Defined in

Mathlib.Algebra.Lie.Abelian

Cited by

4 results in Mathlib

Foundations

Depth 18 from the axioms · uses propext

Assumes

CommRingLieRingLieAlgebraAddCommGroupModuleLieRingModuleLieModule