Theorems · Theorem · nonassociative algebras
LieAlgebra.HasTrivialRadical.eq_bot_of_isSolvable
∀ {R : Type u_1} {L : Type u_2} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L]
[LieAlgebra.HasTrivialRadical R L] (I : LieIdeal R L) [hI : LieAlgebra.IsSolvable ↥I], I = ⊥- Defined in
- Mathlib.Algebra.Lie.Semisimple.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 80 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
- Bot.botstatement · cited by 4,720
- LieRingstatement and proof · cited by 1,548
- LieAlgebrastatement and proof · cited by 1,246
- LieIdealstatement and proof · cited by 282
- LieAlgebra.IsSolvablestatement and proof · cited by 24
- LieAlgebra.HasTrivialRadicalstatement and proof · cited by 11
- sSup_eq_botproof · cited by 7
- LieAlgebra.HasTrivialRadical.radical_eq_botproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- LieAlgebra.hasTrivialRadical_iff_no_solvable_idealsproof · cited by 1