Theorems · Theorem · nonassociative algebras
LieAlgebra.abelian_of_solvable_ideal_eq_bot_iff
∀ {R : Type u} {L : Type v} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L] (I : LieIdeal R L)
[h : LieAlgebra.IsSolvable ↥I], LieAlgebra.derivedAbelianOfIdeal I = ⊥ ↔ I = ⊥- Defined in
- Mathlib.Algebra.Lie.Solvable
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- LieIdealstatement and proof · cited by 282
- IsLieAbelianproof · cited by 55
- LieAlgebra.derivedSeriesOfIdealproof · cited by 28
- LieAlgebra.IsSolvablestatement and proof · cited by 24
- LieAlgebra.derivedLengthOfIdealproof · cited by 5
- LieAlgebra.derivedAbelianOfIdealstatement · cited by 3
- LieAlgebra.derivedSeries_of_derivedLength_succproof · cited by 2
- LieAlgebra.derivedSeries_of_bot_eq_botproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- LieAlgebra.hasTrivialRadical_iff_no_abelian_idealsproof · cited by 0