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Lemma 10.161.11. A Noetherian domain whose fraction field has characteristic zero is N-1 if and only if it is N-2 (i.e., Japanese).

Proof. This is clear from Lemma 10.161.8 since every field extension in characteristic zero is separable. $\square$

Comments (2)

Comment #4965 by Rankeya on

When you say a "Noetherian domain of characteristic 0" do you mean the domain contains the rationals or that its fraction field has characteristic 0? I think this result holds as long as the fraction field of the domain has characteristic 0, so may be it is good to specify this in the statement?

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  • 5 comment(s) on Section 10.161: Japanese rings

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