Definition 47.21.1. Gorenstein rings.

Let $A$ be a Noetherian local ring. We say $A$ is

*Gorenstein*if $A[0]$ is a dualizing complex for $A$.Let $A$ be a Noetherian ring. We say $A$ is

*Gorenstein*if $A_\mathfrak p$ is Gorenstein for every prime $\mathfrak p$ of $A$.

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