Example 3

Tag 0D4U, permanent. Cite it as [Bourbaki, Tag 0D4U].

Commutative Algebra, chapter X, § 3. Profondeur et dimension homologique

Let $A$ be a noetherian local ring, $J$ an ideal of $A$ generated by an $A$ -regular sequence of elements of $m_A$ . If $A/J$ is a Gorenstein ring, then the same is true of $A$ (No. 4, Cor. of Prop. 7).

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

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