TY - JOUR
T1 - Controlling formal fibers of principal prime ideals
AU - Dundon, A.
AU - Jensen, D.
AU - Loepp, S.
AU - Provine, J.
AU - Rodu, J.
PY - 2007
Y1 - 2007
N2 - Let (T, m) be a complete local (Noetherian) ring, S0 the prime subring of T and p≠0 a regular and prime element of T. Given a finite set of incomparable prime ideals C = {Q1,..., Qn} of T such that either Qi ∩ S0 = (0) for all i or Qi ∩ S0 = pS0 for all i, we provide necessary and sufficient conditions for T to be the completion of a local domain A such that p ε{lunate} A and the formal fiber of pA is semi-local with maximal ideals the elements of C. We also show that in a special case the domain A we construct is excellent.
AB - Let (T, m) be a complete local (Noetherian) ring, S0 the prime subring of T and p≠0 a regular and prime element of T. Given a finite set of incomparable prime ideals C = {Q1,..., Qn} of T such that either Qi ∩ S0 = (0) for all i or Qi ∩ S0 = pS0 for all i, we provide necessary and sufficient conditions for T to be the completion of a local domain A such that p ε{lunate} A and the formal fiber of pA is semi-local with maximal ideals the elements of C. We also show that in a special case the domain A we construct is excellent.
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U2 - 10.1216/rmjm/1199649827
DO - 10.1216/rmjm/1199649827
M3 - Article
AN - SCOPUS:40549120317
SN - 0035-7596
VL - 37
SP - 1871
EP - 1891
JO - Rocky Mountain Journal of Mathematics
JF - Rocky Mountain Journal of Mathematics
IS - 6
ER -