Example 3

Tag 0D32, permanent. Cite it as [Bourbaki, Tag 0D32].

Commutative Algebra, chapter X, § 2. Modules et anneaux macaulayens

A normal noetherian ring of dimension $\leqslant 2$ is a Macaulay ring (§ 1, No. 10, text preceding Theorem 4). Conversely, let $A$ be a Macaulay ring whose local ring $A_p$ at every prime ideal $p$ of height $\leqslant 1$ is integrally closed; then A is normal (§ 1, No. 10, Theorem 4).

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

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