Proposition 14

Tag 05KY, permanent. Cite it as [Bourbaki, Tag 05KY].

Algebra, chapter II, § 1. Modules

For a submodule $M$ of a module $E$ to be a direct factor, it is necessary and sufficient that there exist a projector of $E$ whose image is $M$ or a projector of $E$ whose kernel is $M$ .

This follows immediately from no. 8, Proposition 12 and Corollary.

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

Cited by

Corollary 1, § 3
Proposition 15, § 1
Proposition 13, § 8

Cites

no. 8, Proposition 12