Theorems · Theorem · nonassociative algebras
LieAlgebra.LieIdeal.solvable_iff_le_radical
∀ (R : Type u) (L : Type v) [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L] [IsNoetherian R L] (I : LieIdeal R L), LieAlgebra.IsSolvable ↥I ↔ I ≤ LieAlgebra.radical R L
The → direction of this lemma is actually true without the IsNoetherian assumption.
- Defined in
- Mathlib.Algebra.Lie.Solvable
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- LieRingstatement and proof · cited by 1,548
- LieAlgebrastatement and proof · cited by 1,246
- LieIdealstatement and proof · cited by 282
- IsNoetherianstatement and proof · cited by 208
- le_sSupproof · cited by 79
- LieAlgebra.IsSolvablestatement and proof · cited by 24
- LieAlgebra.radicalstatement and proof · cited by 13
- LieAlgebra.le_solvable_ideal_solvableproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- LieAlgebra.abelian_radical_iff_solvable_is_abelianproof · cited by 0
- LieAlgebra.killingCompl_top_le_radicalproof · cited by 0