  For a Dedekind domain $\mathcal{O}$ and a rank two co-torsion module
$M\subseteq \mathcal{O}^2$ with invariant factor ideals $\mathcal{L}\supseteq
\mathcal{K}$ in $\mathcal{O}$, that is, $\frac{\mathcal{O}^2}{M}\cong
\frac{\mathcal{O}}{\mathcal{L}}\oplus \frac{\mathcal{O}}{\mathcal{K}}$ we
associate a new projective space invariant element in
$\mathbb{PF}^1_{\mathcal{I}}$ where $\mathcal{I}$ is given by the ideal
factorization $\mathcal{K} = \mathcal{L}\mathcal{I}$ in $\mathcal{O}$. This
invariant element along with the invariant factor ideals determine the module
$M$ completely as a subset of $\mathcal{O}^2$. As a consequence, projective
spaces associated to ideals in $\mathcal{O}$ can be used to enumerate such
modules. We compute the zeta function associated to such modules in terms of
the zeta function of the one dimensional projective spaces for the ring
$\mathcal{O}_K$ of integers in a number field $K/\mathbb{Q}$ and relate them to
Dedekind zeta function. Using the projective spaces as parameter spaces, we
re-interpret the Chinese remainder reduction isomorphism
$\mathbb{PF}^1_{\mathcal{I}} \rightarrow \underset{i=1}{\overset{l}{\prod}}
\mathbb{PF}^1_{\mathcal{I}_i}$ associated to a factorization of an ideal
$\mathcal{I}=\underset{i=1}{\overset{l}{\prod}} \mathcal{I}_i$ into mutually
co-maximal ideals $\mathcal{I}_i,1\leq i\leq l$ in terms of the intersection of
associated modules arising from the projective space elements.
