Lemma 1

Tag 0008, permanent. Cite it as [Bourbaki, Tag 0008].

Algebra, VIII, p. 3, § 1. Artinian Modules and Noetherian Modules

Let M be a Noetherian A-module and E a subset of M. There exists a finite subset F of E generating the same submodule as E.

Indeed, by VIII, p. 2, there exists a finite subset F of E such that $\sum_{x\in E}Ax=\sum_{x\in F}Ax$ .

Bourbaki sets the proof directly after the statement, and the corpus does not separate them, so what is above is the statement and its proof together.

Cited by

Nothing.

Cites

VIII, p. 2