Let $A$ be an integral domain. Denote by $A'$ the integral closure of $A$ in $\mathsf{Frac} \:A$. Is it true that $A'$ is normal?
2026-03-28 13:32:27.1774704747
The integral closure is normal
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This is more or less a tautology: the integral closure of $A$ in its fraction field is integrally closed (easy exercise), and integrally closed rings are normal (read the section on localization of Atiyah--Macdonald).