 In a PID, nonzero primary ideals are powers of primes, and so formula_16.When formula_17, the resulting indecomposable module is formula_18 itself, and this is inside the part of "M" that is a free module.The summands formula_19 are indecomposable, so the primary decomposition is a decomposition into indecomposable modules, and thus every finitely generated module over a PID is a completely decomposable module.