Definition 10.162.1. Let $R$ be a ring.

1. We say $R$ is universally Japanese if for any finite type ring map $R \to S$ with $S$ a domain we have that $S$ is N-2 (i.e., Japanese).

2. We say that $R$ is a Nagata ring if $R$ is Noetherian and for every prime ideal $\mathfrak p$ the ring $R/\mathfrak p$ is N-2.

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