Proposition 23

Let $A$ be a Dedekind domain and $T$ a finitely generated torsion $A$-module. There exist two finite families $(n_i)_{i \in I}$ and $(\mathfrak{p}_i)_{i \in I}$, where the $n_i$ are integers $\geq 1$ and the $\mathfrak{p}_i$ elements of $P$, such that $T$ is isomorphic to the direct sum $\bigoplus_{i \in I} (A/\mathfrak{p}_i^{n_i})$. Further, the families $(n_i)_{i \in I}$ and $(\mathfrak{p}_i)_{i \in I}$ are unique to within a bijection of the indexing set.

This follows from no. 4, Theorem 5, taking account of the fact that a pseudo-isomorphism is here an isomorphism.