Definition 3

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

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

Let g be a semi-simple Lie algebra. An element x of g is called semi-simple (resp. nilpotent) if, for every g-module M of finite dimension over K, $x_M$ is a semi-simple (resp. nilpotent) endomorphism of M.

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

Cited by

Theorem 2, § 2

Cites

Nothing.