Nagata ring

History

Origin of the term

Grothendieck dubbed these rings as universally Japanese rings. Nagata, in his paper, used the term pseudo-geometric ring. Nowadays, the term Nagata ring is most commonly used.

Definition

Symbol-free definition

An integral domain is termed a Nagata ring if every quotient ring that is an integral domain is a Japanese ring. Nagata rings are also termed pseudo-geometric rings and universally Japanese rings.