Normal ring

Definition
A commutative unital ring is said to be normal if it is a reduced ring and further, if it is integrally closed in its total quotient ring.

This generalizes the notion of normal domain where we require the integral domain to be integrally closed in its field of fractions.

Metaproperties
The localization of a normal ring at any multiplicatively closed subset not containing zero, and hence, in particular, the localization relative to any prime ideal, is again a normal ring.

The polynomial ring over a normal ring is a normal ring.