Theorems · Theorem · nonassociative algebras
LieModule.nilpotencyLength_eq_zero_iff
∀ (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 = 0 ↔ Subsingleton M
- Defined in
- Mathlib.Algebra.Lie.Nilpotent
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- AddCommGroupstatement and proof · cited by 12,871
- Set.ofPredproof · cited by 6,101
- Bot.botproof · cited by 4,720
- Set.Nonemptyproof · cited by 2,627
- LieRingstatement and proof · cited by 1,548
- InfSet.sInfproof · cited by 935
- LieRingModulestatement and proof · cited by 727
- LieSubmoduleproof · cited by 489
- LieModule.lowerCentralSeriesproof · cited by 60
- LieModule.IsNilpotentstatement and proof · cited by 46
- subsingleton_iff_bot_eq_topproof · cited by 16
Cited by1
Results whose statement or proof uses this declaration.
- LieModule.nontrivial_lowerCentralSeriesLastproof · cited by 2