Proposition 6

Tag 000Q, permanent. Cite it as [Bourbaki, Tag 000Q].

Algebra, VIII, p. 9, § 1. Artinian Modules and Noetherian Modules

Let M be an Artinian (resp. Noetherian) left A-module with finitely generated countermodule. The ring of homotheties $A_M$ of M is left Artinian (resp. left Noetherian).

This follows from Lemma 4 and Proposition 3 of VIII, p. 3.

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

Corollary, § 1
Remark, § 1
Exercise 11, § 10
Remark, § 3

Cites

Lemma 4
Proposition 3 of VIII, p. 3