Theorems · Theorem · nonassociative algebras

LieModule.isFaithful_iff_ker_eq_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] [inst_6 : LieModule R L M],
  LieModule.IsFaithful R L M ↔ LieModule.ker R L M = ⊥

Defined in

Mathlib.Algebra.Lie.Abelian

Cited by

2 results in Mathlib

Foundations

Depth 53 from the axioms · uses propext, Quot.sound

Assumes

CommRingLieRingLieAlgebraAddCommGroupModuleLieRingModuleLieModule