This M.Sc. thesis is based on the following paper A. Facchini and Z. Nazemian, Serial Factorizations of Right Ideals. Journal of Pure and Applied Algebra ,???, (????) ????-????. The work in this thesis is prompted by the idea of extending of Dedekind domains. In fact, In a Dedekind domain D, every non-zero proper ideal A factors as a product A = P? t?P? t?:::Pk tk of distinct prime ideals Pi. For a Dedekind domain D, the D-modules D=Pi ti are uniserial. We extend this property studying suitable factorizations A = A?A?:::An of a right ideal A of an arbitary ring R as a product of proper right ideals A?,...,An with all the modules R=Ai uniserial modules. At the first we discribe the difinition of a finite set coindependent. کلیدواژه فارسی