  A resolution of the intersection of a finite number of subgroups of an
abelian group by means of their sums is constructed, provided the lattice
generated by these subgroups is distributive. This is used for detecting
singularities of modules over Dedekind rings. A generalized Chinese remainder
theorem is derived as a consequence of the above resolution. The
Gelfand-Naimark duality between finite closed coverings of compact Hausdorff
spaces and the generalized Chinese remainder theorem is clarified.
