Controlling formal fibers of principal prime ideals

A. Dundon, D. Jensen, S. Loepp, J. Provine, J. Rodu

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

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.

Original languageEnglish
Pages (from-to)1871-1891
Number of pages21
JournalRocky Mountain Journal of Mathematics
Volume37
Issue number6
DOIs
StatePublished - 2007

ASJC Scopus subject areas

  • Mathematics (all)

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