Completions of Local Rings with an Isolated Singularity Original Research Article

It is shown that all equicharacteristic complete local rings can be realized as completions of local rings whose proper localizations are all regular. The only restriction in the mixed characteristic case is that the prime integer cannot be a nonzero zerodivisor in any proper localization of the complete ring. The constructed examples are unique factorization domains whenever possible and in general are as close to being UFDs as the hypothesis will allow.