Lemma 10.36.5. Let $R \to S$ be a ring map. The following are equivalent

$R \to S$ is finite,

$R \to S$ is integral and of finite type, and

there exist $x_1, \ldots , x_ n \in S$ which generate $S$ as an algebra over $R$ such that each $x_ i$ is integral over $R$.

## Comments (0)

There are also: