Corollary 1

Tag 04O9, permanent. Cite it as [Bourbaki, Tag 04O9].

If $A$ is a Noetherian ring, the $A$ -module $A'$ is finitely generated and in particular the ring $A'$ is Noetherian.

$A'$ is a submodule of a finitely generated $A$ -module.

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

Cited by

Nothing.