Kaplansky’s problem on valuation rings

Laszlo Fuchs, Saharon Shelah

Research output: Contribution to journalArticlepeer-review

31 Scopus citations

Abstract

The following theorem is proved in ZFC: there exist valuation rings which are not surjective homomorphic images of valuation domains. The proof relies on the existence of nonstandard divisible uniserial modules in ZFC.

Original languageEnglish
Pages (from-to)25-30
Number of pages6
JournalProceedings of the American Mathematical Society
Volume105
Issue number1
DOIs
StatePublished - Jan 1989

Keywords

  • Divisible modules
  • First order model
  • Forcing
  • Nonstandard uniserials
  • Uniserial
  • Valuation domains
  • Valuation rings
  • Zfc

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