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As we know every normal Noetherian domain $ R$ can be written as $ $ R=\bigcap_{\mathsf{ht}(\mathfrak p)=1}R_\mathfrak p.$ $ I’m asking myself the following question: Question: If the normalization of $ \widetilde{R}$ is given by $ $ \widetilde{R}=\bigcap_{\mathsf{ht}(\mathfrak p)=1}R_\mathfrak p,$ $ then is $ R$ normal? Every reference or counterexample is well accepted.Read more