Remark 2

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

Commutative Algebra, chapter X, § 9. Modules dualisants

Let $\Omega$ be a dualizing $A$ -module; for every projective $A$ -module $L$ of rank 1, the $A$ -module $\Omega \otimes_A L$ is dualizing (A, X, p. 108, prop. 7, b)). We shall see below (No. 4, prop. 6) that every dualizing $A$ -module is isomorphic to a module of this form.

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

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