Definition 1

Tag 09ZA, permanent. Cite it as [Bourbaki, Tag 09ZA].

Lie Groups and Lie Algebras, chapter I, § 6. Semi-simple Lie algebras

Let g be a Lie algebra. g is called semi-simple if and only if the only commutative ideal of g is {0}.

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

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