Gorenstein Singularities

Definition

A local ring \((R,\frakm, k)\) is a Gorenstein ring if any of the following equivalent conditions are met:

• \(R\) has finite injective dimension \(n\) as an \(R\)-module
• \(\Ext_R^i(k, R) = 0\) for \(i \neq n\) and is \(k\) when \(i = n\)