If $R\subseteq R'$ are integral extensions of Dedekind rings, and $0\neq\mathfrak p$ is a prime ideal of $R$ then $R'\mathfrak p\neq R'$.
Do you know an example $R'\mathfrak p=R'$?. Of course $R\subseteq R'$ is not integral.
Thank you all.
2026-03-25 23:38:07.1774481887
Factorization of a prime ideal in a integral extension.
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Does $R=\Bbb Z$, $R'=\Bbb Z[\frac17]$, and $\mathfrak p=7\Bbb Z$ work?