| Affiliation: | Department of Mathematics, Stanford University, Building 380, Stanford, California 94305-2125 ; Department of Mathematics, P.O. Box 400137, University of Virginia, Charlottesville, Virginia 22904-4137 ; P.O. Box 372, Webb, Mississippi 38966 ; Department of Mathematics, MIT, 77 Massachusetts Ave., Cambridge, Massachusetts 02139 |
| Abstract: | We find necessary and sufficient conditions for a complete local ring to be the completion of a reduced local ring. Explicitly, these conditions on a complete local ring  with maximal ideal  are (i)  or  , and (ii) for all  , if  is an integer of  , then  . |
