Theorems · Theorem · nonassociative algebras
LieAlgebra.abelian_iff_derived_one_eq_bot
∀ {R : Type u} {L : Type v} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L] (I : LieIdeal R L),
IsLieAbelian ↥I ↔ LieAlgebra.derivedSeriesOfIdeal R L 1 I = ⊥- Defined in
- Mathlib.Algebra.Lie.Solvable
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingLieRingLieAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Bot.botstatement and proof · cited by 4,720
- LieRingstatement and proof · cited by 1,548
- LieAlgebrastatement and proof · cited by 1,246
- Bracket.bracketproof · cited by 642
- LieIdealstatement and proof · cited by 282
- IsLieAbelianstatement and proof · cited by 55
- LieAlgebra.derivedSeriesOfIdealstatement · cited by 28
- LieAlgebra.derivedSeriesOfIdeal_succproof · cited by 14
- LieAlgebra.derivedSeriesOfIdeal_zeroproof · cited by 6
- LieSubmodule.lie_abelian_iff_lie_self_eq_botproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- LieAlgebra.abelian_iff_derived_succ_eq_botproof · cited by 1