Corollary 2

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

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

The nilradical of a Noetherian ring A is the intersection of the ideals $\mathfrak{p} \in \operatorname{Ass}(A)$ .

We know that the nilradical of A is the intersection of the minimal elements of $\operatorname{Spec}(A) = \operatorname{Supp}(A)$ (Chapter II, § 2, no. 6, Proposition 13).

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

Cited by

Proposition 10, § 2

Cites

Chapter II, § 2, no. 6, Proposition 13