Example 6

Tag 0CK2, permanent. Cite it as [Bourbaki, Tag 0CK2].

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

Let $k$ be a field and $A$ a nonzero integral $k$ -algebra. Then one has $\dim(A) = 0$ . This results from cor. 1 to prop. 1 of V, § 2, No. 1, and from the fact that $\dim(k) = 0$ .

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

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