Definition 47.21.1. Gorenstein rings.

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

2. Let $A$ be a Noetherian ring. We say $A$ is Gorenstein if $A_\mathfrak p$ is Gorenstein for every prime $\mathfrak p$ of $A$.

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).