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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1993-1102888-9
PII: S 0002-9947(1993)1102888-9
Article copyright: © Copyright 1993 American Mathematical Society