Corollary

Tag 00R1, permanent. Cite it as [Bourbaki, Tag 00R1].

A generating A-module is faithful.

Let $a\in A$ satisfy $aM = 0$ . Using the implication (i) $\Rightarrow$ (iv) of Theorem 1, we obtain $aA_s= 0$ , and therefore $a= 0$ . The corollary follows (II, §1, No. 12, p. 219).

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

Proposition 4, § 8

Cites

II, §1, No. 12, p. 219
Theorem 1