Theorems · Theorem · nonassociative algebras
LieAlgebra.center_le_radical
∀ (R : Type u) (L : Type v) [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L], LieAlgebra.center R L ≤ LieAlgebra.radical R L
- Defined in
- Mathlib.Algebra.Lie.Solvable
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 83 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.
Cites8
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 · cited by 282
- le_sSupproof · cited by 79
- LieAlgebra.IsSolvableproof · cited by 24
- LieAlgebra.centerstatement and proof · cited by 23
- LieAlgebra.radicalstatement · cited by 13
Cited by2
Results whose statement or proof uses this declaration.
- LieAlgebra.hasCentralRadical_and_of_isIrreducible_of_isFaithfulproof · cited by 1
- LieAlgebra.hasCentralRadical_of_radical_leproof · cited by 0