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Theorems · Theorem · nonassociative algebras

LieAlgebra.hasTrivialRadical_of_no_solvable_ideals

∀ {R : Type u_1} {L : Type u_2} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L],
  (∀ (I : LieIdeal R L), LieAlgebra.IsSolvable ↥I → I = ⊥) → LieAlgebra.HasTrivialRadical R L
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
Assumes
CommRingLieRingLieAlgebra
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

LieAlgebra.hasTrivialRadical_iff_no_solvable_ideals · cited by 1LieAlgebra.hasTrivialRadi…CommRing · cited by 17173CommRingBot.bot · cited by 4720Bot.botLieRing · cited by 1548LieRingLieAlgebra · cited by 1246LieAlgebraLieIdeal · cited by 282LieIdealLieAlgebra.IsSolvable · cited by 24LieAlgebra.IsSolvableLieAlgebra.HasTrivialRadical · cited by 11LieAlgebra.HasTrivialRadi…sSup_eq_bot · cited by 7sSup_eq_botLieAlgebra.hasTrivialRadical_…CITED BYCITES

Cites8

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Cited by1

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