Lemma 10.39.16. Let R \to S be a flat ring map. The following are equivalent:
R \to S is faithfully flat,
the induced map on \mathop{\mathrm{Spec}} is surjective, and
any closed point x \in \mathop{\mathrm{Spec}}(R) is in the image of the map \mathop{\mathrm{Spec}}(S) \to \mathop{\mathrm{Spec}}(R).
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