Definition 6

Tag 076N, permanent. Cite it as [Bourbaki, Tag 076N].

Algebra, chapter VII, § 5. Endomorphisms of vector spaces

— Let E be a finite dimensional vector space over a commutative field K. Then an endomorphism u of E is said to be semi-simple if every subspace of E which is closed under u has a complement which is closed under u.

This means that every submodule of the $K[X]$ -module E, is a direct factor, in other words the $K[X]$ -module $E_u$ is semi-simple (VII, p. 9).

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

Cited by

Nothing.

Cites

VII, p. 9