Proposition 1

Tag 04J8, permanent. Cite it as [Bourbaki, Tag 04J8].

For every prime ideal $p$ of a ring $A$ and every submodule $M \neq 0$ of $A/p$ , $\operatorname{Ass}(M) = \{p\}$ .

As the ring $A/p$ is an integral domain, the annihilator of an element $\neq 0$ of $A/p$ is $p$ .

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

Cited by

Nothing.