Characterization of completions of unique factorization domains

Heitmann, Raymond C.

doi:10.1090/S0002-9947-1993-1102888-9

Characterization of completions of unique factorization domains
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by Raymond C. Heitmann

Trans. Amer. Math. Soc. 337 (1993), 379-387

DOI: https://doi.org/10.1090/S0002-9947-1993-1102888-9

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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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