Corollary 1

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

Commutative Algebra, chapter IV, § 2. Primary decomposition

If A is Noetherian and $\mathfrak{P} \in \operatorname{Ass}_B(E \otimes_A F)$ , then $\rho^{-1}(\mathfrak{P}) \in \operatorname{Ass}_A(E)$ and $\rho^{-1}(\mathfrak{P})$ is the only prime ideal $p$ of A such that $\mathfrak{P} \in \operatorname{Ass}_B(F/pF)$ .

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

Cited by

Remark, § 2

Cites

Nothing.