45 research outputs found
Semilocal Generic Formal Fibers
Let T be a complete local ring and C a finite set of incomparable prime
ideals of T. We find necessary and sufficient conditions for T to be the
completion of an integral domain whose generic formal fiber is semilocal with
maximal ideals the elements of C. In addition, if char T = 0, we give necessary
and sufficient conditions for T to be the completion of an excellent integral
domain whose generic formal fiber is semilocal with maximal ideals the elements
of C.Comment: 15 page
Characterization of completions of excellent domains of characteristic zero
AbstractWe show that a complete local ring T containing the integers is the completion of a local excellent integral domain if and only if it is reduced, equidimensional, and no integer of T is a zero divisor
Gluing Associated Prime Ideals of Small Height
Let be a local (Noetherian) ring and suppose that has associated
prime ideals where . We identify sufficient conditions for there to
exist a local (Noetherian) subring of such that and have the
same completion and has exactly associated prime ideals. We include
applications and consequences of this result.Comment: 14 page