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|Paper IPM / M / 15697||
In a Dedekind domain D, every non-zero proper ideal A factors as a product A=P1t1…Pktk of powers of distinct prime ideals Pi. For a Dedekind domain D, the D-modules D/Piti are uniserial. We extend this property studying suitable factorizations A=A1... An of a right ideal A of an arbitrary ring R as a product of proper right ideals A1,...,An with all the modules R/Ai 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 h-local Prüfer domains and that of semirigid commutative GCD domains.
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