COMPLETIONS OF HYPERSURFACE DOMAINS
Let V be a complete regular local (Noetherian) ring and let f is an element of V be a nonunit. We find necessary and sufficient conditions for V/fV to be the completion with respect to the maximal ideal of an integral domain of the form S/fV boolean AND S where S is a regular local ring whose completion with respect to its maximal ideal is V. In addition, if V/fV contains the rationals, we give necessary and sufficient conditions for V/fV to be the completion of an excellent local domain of the form S/fS, where f is an element of S, and S is a regular local ring whose completion is V.
hypersurface complete local ring excellent ring