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## Lemma of Hironaka in Hartshorne III.9.12

In the proof, the author consider the normalization $\tilde{A}$ of $A$ and show $\tilde{A}/t \tilde{A}$ is a integral domain. He showed that the localizations at points of Spec $A$ are domains, but we know a non-domain ring can have integral localizations. How should I understand the proof? Thanks a lot.

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 Thank for Schwede's edit. – MZWang Feb 5 2012 at 10:30 I don't understand your question: $A$ is supposed to be a local noetherian domain -- so he doesn't have to work to prove it is a domain! – Julien Puydt Aug 26 at 14:47 Julien, the problem is to show $\tilde{A}/t\tilde{A}$ is a domain. – MZWang Aug 30 at 3:32