Theorems · Theorem · nonassociative algebras
LieModule.isTrivial_of_nilpotencyLength_le_one
∀ (L : Type v) (M : Type w) [inst : LieRing L] [inst_1 : AddCommGroup M] [inst_2 : LieRingModule L M] [LieModule.IsNilpotent L M], LieModule.nilpotencyLength L M ≤ 1 → LieModule.IsTrivial L M
- Defined in
- Mathlib.Algebra.Lie.Nilpotent
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommGroupstatement and proof · cited by 12,871
- Nontrivialproof · cited by 2,416
- LieRingstatement and proof · cited by 1,548
- LieRingModulestatement and proof · cited by 727
- LieModule.IsNilpotentstatement and proof · cited by 46
- LieModule.IsTrivialstatement · cited by 14
- LieModule.nilpotencyLengthstatement and proof · cited by 7
- LieModule.nilpotencyLength_eq_one_iffproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- LieModule.lowerCentralSeriesLast_le_of_not_isTrivialproof · cited by 1