Let $A$ be a Dedekind domain, and let $P$ be a finitely generated projective $A$-module of positive constant rank $r$. Then there exists an invertible ideal $I \trianglelefteq A$ such that
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\begin{align*}
P \cong A^{r-1} \oplus I
\end{align*}
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as $A$-modules. Moreover, if $I$ and $J$ are invertible ideals of $A$, then
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\begin{align*}
A^{r-1} \oplus I \cong A^{r-1} \oplus J
\end{align*}
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as $A$-modules if and only if $I$ and $J$ represent the same class in $\operatorname{Pic}(A)$.