Corollary 1 (Hilbert)

Tag 00RW, permanent. Cite it as [Bourbaki, Tag 00RW].

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

Let A be a Noetherian commutative ring. For every integer $n\geqslant 0$ , the polynomial algebra $A[X_1, . . . ,X_n]$ is a Noetherian ring.

This follows by induction from Theorem 2, taking Proposition 8 of III, §2, No. 9, p. 453, into account.

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 2, § 1

Cites

Proposition 8 of III, §2, No. 9, p. 453 not in this corpus
Theorem 2