Constructing almost excellent unique factorization domains

John Bryk, Sonja Mapes*, Charles Samuels, Grace Wang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


Let (T, M) be a complete local normal integral domain containing the rationals such that |T/M| ≥ c where c is the cardinality of the real numbers. Let p be a non-maximal prime ideal of T such that Tp is a regular local ring. We construct a local Unique Factorization Domain (UFD) A such that the M-adic completion of A is T, p is maximal in the generic formal fiber and all fibers of A are geometrically regular except for those over some height one prime ideals.

Original languageEnglish (US)
Pages (from-to)1321-1336
Number of pages16
JournalCommunications in Algebra
Issue number5
StatePublished - 2005


  • Complete ring
  • Completion
  • Excellent ring
  • Local integral domain
  • Normal domain
  • Unique factorization domain

ASJC Scopus subject areas

  • Algebra and Number Theory


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