Gorenstein ring

A **Gorenstein ring** is a type of commutative ring that has particularly nice homological properties. More formally, a Noetherian ring \( R \) is called Gorenstein if it satisfies the following equivalent conditions: 1. **Dualizing Complex**: The singularity category of \( R \) has a dualizing complex which is concentrated in non-negative degrees, and the homological dimension of the ring is finite.