Why do they call these rings 'N-1' and 'N-2'? What is the reason behind this terminology?

> **Definition** ([Tag 032F](https://stacks.math.columbia.edu/tag/032F)). Let $R$ be a domain with field of fractions $K$.
> 1. We say $R$ is *N-1* if the integral closure of $R$ in $K$
is a finite $R$-module.
> 2. We say $R$ is *N-2* or *Japanese* if for any finite
extension $L/K$ of fields the integral closure of $R$ in $L$
is finite over $R$.

(I guess the 'Japanese' terminology for the latter is to pay tribute to the Japanese mathematicians that studied these kinds of rings properties, such as Masayoshi Nagata.)