Characterization of Completions of Unique Factorization Domains

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.

Locations

• Transactions of the American Mathematical Society - View - PDF