Definition 3

Tag 09Y7, permanent. Cite it as [Bourbaki, Tag 09Y7].

Lie Groups and Lie Algebras, chapter I, § 5. Solvable Lie algebras

Let $g$ be a Lie algebra. The nilpotent radical of $g$ is the intersection of the kernels of the finite-dimensional simple representations of $g$ .

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

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