Normal ring

Summary

A normal ring is a commutative ring whose localization at every prime ideal is an integrally closed domain. It is the local form of integral closedness, and it allows rings that are not domains, such as products of integrally closed domains. A Noetherian normal ring is a finite product of integrally closed domains. Normal rings are the rings of functions on normal schemes, and normality is described by Serre's criterion.