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The derived exact sequences.- Finite modules.- Realization of finite modules.- ?i of finite modules.- Product structure on finite modules.- Classification of derived product structure.- Rational invariants.- Z-torsion-free modules.- ?-only torsion.- Statement of realization theorem.- Inductive construction of derived sequences.- Inductive recovery of derived sequences.- Homogeneous and elementary modules.- Realization of elementary modules.- Classification of elementary modules.- Completion of proof.- Classification of ?-primary modules.- Classification fails in degree 4.- Product structure on ?-primary modules.- Classification of product structure.- Realization of product structure on homogeneous modules.- Product structure on semi-homogeneous modules.- A non-semi-homogeneous module.- Rational classification of product structure.- Non-singular lattices over a Dedekind domain.- Norm criterion for a non-singular lattice.- Dedekind criterion: p-adic reduction.- A computable Dedekind criterion.- Computation of low-degree cases.- Determination of ideal class group.- The quqdratic symetric case.