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

$S$ is geometrically integral over $k$,

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

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

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Comment #4940 by Rankeya on

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