Regular ring

Definition
A Noetherian ring is termed a regular ring if its localization at any prime ideal is a regular local ring.

Stronger properties

 * Regular local ring

Weaker properties

 * Cohen-Macaulay ring:
 * Universally catenary ring
 * Catenary ring
 * Noetherian ring

Spectrum
The spectrum of a regular ring has the fairly strong property that every connected component is irreducible. Thus, any regular ring is a direct product of integral domains. If we localize at a point, it should be an integral domain.