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Lemma 10.49.3. 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 $S \otimes _ k k'$ is a domain,

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

Comments (2)

Comment #4940 by Rankeya on

should be in this statement.

There are also:

  • 6 comment(s) on Section 10.49: Geometrically integral algebras

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