Corollary 2

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

Algebra, chapter II, § 1. Modules

For a family $(a_t)_{t \in T}$ of elements of an A-module E to be a generating system of E, it is necessary and sufficient that the linear mapping $A_s^{(T)} \to E$ determined by this family be surjective.

This is just another way of expressing Proposition 9 of no. 7.

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

Cited by

Definition 10, § 1
Remark, § 1
Proposition 20, § 1
Proposition 1, § 8

Cites

Proposition 9