Corollary 1

Tag 0DC4, permanent. Cite it as [Bourbaki, Tag 0DC4].

Commutative Algebra, chapter X, § 9. Modules dualisants

In order that $A$ be a Gorenstein ring, it is necessary and sufficient that the $A$ -module $\Omega$ be projective of rank 1.

This follows from Example 2 of No. 1 and Proposition 7 c).

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

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