Source: wikibot/gorenstein-ring
= Gorenstein ring
{wiki=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.