  Given a graph whose edges are labeled by ideals in a ring, a generalized
spline is a labeling of each vertex by a ring element so that adjacent vertices
differ by an element of the ideal associated to the edge. We study splines over
the ring Z/mZ. Previous work considered splines over domains, in which very
different phenomena occur. For instance when the ring is the integers, the
elements of bases for spline modules are indexed by the vertices of the graph.
However we prove that over Z/mZ spline modules can essentially have any rank
between 1 and n. Using the classification of finite Z-modules, we begin the
work of classifying splines over Z/mZ and produce minimum generating sets for
splines on cycles over Z/mZ. We close with many open questions.
