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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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