Corollary 2

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

Algebra, VIII, p. 12, § 1. Artinian Modules and Noetherian Modules

Let A be a Noetherian commutative ring. A commutative A-algebra generated by finitely many elements is a Noetherian ring.

Such an algebra is isomorphic to an algebra of the form $A[X_1, . . . ,X_n]/\mathfrak{a}$ , where $n\geqslant 0$ and $\mathfrak{a}$ is an ideal of $A[X_1, . . . ,X_n]$ . We then apply Corollary 1 and Proposition 5 of VIII, p. 7.

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 3, § 1

Cites

Proposition 5 of VIII, p. 7
Corollary 1