Remark

Tag 00U0, permanent. Cite it as [Bourbaki, Tag 00U0].

Lie Groups and Lie Algebras, chapter VII, § 2. Cartan subalgebras and regular elements of a Lie algebra

$\mathscr{C}_{\infty}\mathfrak{g}$ is the smallest ideal $\mathfrak{n}$ of $\mathfrak{g}$ such that the centre of $\mathfrak{g}/\mathfrak{n}$ is zero; it is a characteristic and nilpotent ideal of $\mathfrak{g}$ .

Bourbaki sets the proof directly after the statement, and the corpus does not separate them, so what is above is the statement and its proof together.

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