Theorems · Theorem · nonassociative algebras
LieAlgebra.killingCompl_top_le_radical
∀ (R : Type u_1) (L : Type u_2) [inst : CommRing R] [CharZero R] [IsDomain R] [inst_3 : LieRing L] [inst_4 : LieAlgebra R L] [IsNoetherian R L] [Module.Free R L], LieIdeal.killingCompl R L ⊤ ≤ LieAlgebra.radical R L
The Killing radical of a finite-dimensional Lie algebra is contained in the solvable radical.
- Defined in
- Mathlib.Algebra.Lie.CartanCriterion
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 182 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites17
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
- Top.topstatement and proof · cited by 9,680
- IsDomainstatement and proof · cited by 2,196
- LieRingstatement and proof · cited by 1,548
- LieAlgebrastatement and proof · cited by 1,246
- CharZerostatement and proof · cited by 932
- Bracket.bracketproof · cited by 642
- Module.Freestatement and proof · cited by 597
- LieIdealstatement · cited by 282
- IsNoetherianstatement and proof · cited by 208
- LieAlgebra.radicalstatement · cited by 13
- LieSubmodule.mem_topproof · cited by 11
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