Example 8

Tag 0CK4, permanent. Cite it as [Bourbaki, Tag 0CK4].

Commutative Algebra, chapter VIII, § 1. Dimension de Krull d’un anneau

There exist noetherian rings of infinite dimension (p. 83, exercise 13). We shall see below (§ 3, No. 1, cor. 1 to prop. 2) that every noetherian local ring is of finite dimension.

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

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