Abstract
Let (T,M) be a complete local (Noetherian) unique factorization domain of dimension at least two such that the cardinality of the residue fieldT/Mis at least the cardinality of the real numbers. Suppose (0)=p0⊂p1⊂···⊂pn≠Mis a chain of distinct prime ideals ofTsuch thatpnintersected with the prime subring ofTis the zero ideal. We construct a chain of local unique factorization domainsAn⊂An−1⊂···⊂A1⊂A0=Tsuch that the completion of eachAiisTand for everyithe generic formal fiber ofAiis local (this means that the ringT⊗AiKiis a local ring whereKiis the quotient field ofAi) withpi⊗AiKiits maximal ideal.
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