Theorems · Theorem · nonassociative algebras
LieModule.nilpotencyLength_eq_one_iff
∀ (L : Type v) (M : Type w) [inst : LieRing L] [inst_1 : AddCommGroup M] [inst_2 : LieRingModule L M] [Nontrivial M], LieModule.nilpotencyLength L M = 1 ↔ LieModule.IsTrivial L M
- Defined in
- Mathlib.Algebra.Lie.Nilpotent
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Bot.botproof · cited by 4,720
- Nontrivialstatement and proof · cited by 2,416
- LieRingstatement and proof · cited by 1,548
- LieRingModulestatement and proof · cited by 727
- LieModule.lowerCentralSeriesproof · cited by 60
- LieModule.IsTrivialstatement and proof · cited by 14
- LieModule.nilpotencyLengthstatement · cited by 7
- LieModule.nilpotencyLength_eq_succ_iffproof · cited by 3
- LieModule.trivial_iff_lower_central_eq_botproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- LieModule.isTrivial_of_nilpotencyLength_le_oneproof · cited by 1