Distributive lattices and cohomology

Understand

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.