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 subset of p1 subset of ··· subset of 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 subset of An−1 subset of ··· subset of A1 subset of A0 = Tsuch that the completion of eachAiisTand for everyithe generic formal fiber ofAiis local (this means that the ringT circle times operatorAi Kiis a local ring whereKiis the quotient field ofAi) withpi circle times operatorAi Kiits maximal ideal.
