Let $A$ be a Noetherian domain and $K$ its field of quotients. I would like to prove that, given $x \in K$, we have $x \in A$ iff $x\in A_p$ for every $p$ prime ideal associated to an $y\in A$, $y\ne0$.
2026-03-25 01:24:58.1774401898
Noetherian domain and localization
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