Let $R$ be a commutative, Dedekind (and therefore Noetherian) ring with $1$. Let $I$ be a non-prime ideal of $R$, and let $a,b$ be elements of $R$ such that $a\not\in I,b\not\in I$ but $ab\in I$. Let $\cal P$ be the set of prime ideals appearing in the Dedekind factorization of $(I,a)$ or $(I,b)$. Then $\cal P$ is finite, and I ask : is it always true that some ideal in $\cal P$ must appear in the Dedekind factorization of $I$ ?
If true, this would provide a theoretical "algorithm" to compute the Dedekind factorization of any ideal of such a ring $R$.