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

Definition (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.)