In a Dedekind domain D, every nonzero proper ideal A factors as a product A=P_{1}^{t1}…P_{k}^{tk} of powers of distinct prime ideals P_{i}. For a Dedekind domain D, the Dmodules D/P_{i}^{ti} are uniserial. We extend this property studying suitable factorizations A=A_{1}... A_{n} of a right ideal A of an arbitrary ring R as a product of proper right ideals A_{1},...,A_{n} with all the modules R/A_{i} uniserial modules. When such factorizations exist, they are unique up to the order of the factors. Serial factorizations turn out to have connections with the theory of hlocal Prüfer domains and that of semirigid commutative GCD domains.
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