Definition 1

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

Lie Groups and Lie Algebras, chapter VII, § 5. Decomposable linear Lie algebras

Let $\mathfrak{g}$ be a Lie subalgebra of $\mathfrak{g}\mathfrak{l}(V)$ . Then $\mathfrak{g}$ is said to be decomposable if $\mathfrak{g}$ contains the semi-simple and nilpotent components of each of its elements (Algebra, Chap. VII, §5, no. 8).

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.

Cited by

Definition 1, § 10

Cites

Algebra, Chap. VII, §5, no. 8