Definition 10.37.3. Let $R$ be a domain.

1. An element $g$ of the fraction field of $R$ is called almost integral over $R$ if there exists an element $r \in R$, $r\not= 0$ such that $rg^ n \in R$ for all $n \geq 0$.

2. The domain $R$ is called completely normal if every almost integral element of the fraction field of $R$ is contained in $R$.

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