Lemma 10.48.3. Let $k$ be a field. Let $S$ be a $k$-algebra. The following are equivalent

1. $S$ is geometrically integral over $k$,

2. for every finite extension $k'/k$ of fields the ring $R \otimes _ k k'$ is a domain,

3. $R \otimes _ k \overline{k}$ is a domain where $\overline{k}$ is the algebraic closure of $k$.

Comment #4940 by Rankeya on

$R$ should be $S$ in this statement.

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