Gorenstein ring

Summary

A Gorenstein ring is a Noetherian ring whose local rings have finite injective dimension as modules over themselves. Gorenstein rings sit between complete intersection rings and Cohen–Macaulay rings: every complete intersection is Gorenstein and every Gorenstein ring is Cohen–Macaulay. They are exactly the Cohen–Macaulay local rings whose canonical module is the ring itself, which makes duality statements particularly clean.