Let $R$ be a Noetherian domain. Let $\mathcal S:=\{P \in\mathrm{Spec}(R) : P \in \mathrm{Ass}(R/xR)$, for some $ 0\ne x \in R\}$. Then how to show that $\cap_{P\in \mathcal S} R_P \subseteq R$ ?
2026-02-22 21:30:33.1771795833
Associated primes to principal ideals in a Noetherian domain
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