Let $A$ be a Dedekind domain. Let $\wp$ be a prime ideal in $A$. Can one find pair-wise different prime ideals $\wp_2$,..., $\wp_s$, also different from $\wp$, such that their product $\wp\wp_2 \cdots \wp_s$ is principal?
If not, is this true if we assume further that the ideal class group of $A$ is finite?
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