Corollary

Tag 04JP, permanent. Cite it as [Bourbaki, Tag 04JP].

Commutative Algebra, chapter IV, § 1. Prime ideals associated with a module

If M is a finitely generated module over a Noetherian ring A, Ass(M) is finite.

Under the conditions of Theorem 2, the set $\{p_0, \ldots, p_{n-1}\}$ is not necessarily determined uniquely by M; in particular it may be distinct from Ass(M) (Exercise 6).

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

Cited by

Theorem 1, § 2

Cites

Exercise 6
Theorem 2