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Transactions of the American Mathematical Society

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Characterization of completions of unique factorization domains

Author: Raymond C. Heitmann
Journal: Trans. Amer. Math. Soc. 337 (1993), 379-387
MSC: Primary 13B35; Secondary 13C15, 13F15
MathSciNet review: 1102888
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Abstract: It is shown that a complete local ring is the completion of a unique factorization domain if and only if it is a field, a discrete valuation ring, or it has depth at least two and no element of its prime ring is a zerodivisor. It is also shown that the Normal Chain Conjecture is false and that there exist local noncatenary UFDs.

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Article copyright: © Copyright 1993 American Mathematical Society

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