Theorems · Theorem · nonassociative algebras
LieAlgebra.subsingleton_of_hasTrivialRadical_lie_abelian
∀ (R : Type u_1) (L : Type u_2) [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L] [LieAlgebra.HasTrivialRadical R L] [h : IsLieAbelian L], Subsingleton L
An abelian Lie algebra with trivial radical is trivial.
- Defined in
- Mathlib.Algebra.Lie.Semisimple.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites11
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.topproof · cited by 9,680
- LieRingstatement and proof · cited by 1,548
- LieAlgebrastatement and proof · cited by 1,246
- LieIdealproof · cited by 282
- IsLieAbelianstatement and proof · cited by 55
- LieAlgebra.HasTrivialRadicalstatement and proof · cited by 11
- subsingleton_of_bot_eq_topproof · cited by 8
- LieSubmodule.subsingleton_iffproof · cited by 4
- LieAlgebra.center_eq_botproof · cited by 3
- LieAlgebra.isLieAbelian_iff_center_eq_topproof · cited by 2
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