Corollary 2

Tag 0E1E, permanent. Cite it as [Bourbaki, Tag 0E1E].

Algebra, chapter X, § 8. Dimension homologique

Let $K$ be a commutative field (resp. a principal ideal domain or a Dedekind ring which is not a field). Then $dh(K[X_1, ..., X_n])$ is equal to $n$ (resp. $n + 1$ ). This follows from the fact that $dh(K) = 0$ (resp. $dh(K) = 1$ ).

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

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