The kaplansky test problems for ni-separable groups

Paul C. Eklof*, Saharon Shelah

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

26 Scopus citations

Abstract

We answer a long-standing open question by proving in ordinary set theory, ZFC, that the Kaplansky test problems have negative answers for Ni-separable abelian groups of cardinality NI. In fact, there is an Ni-separable abelian group M such that M is isomorphic to M⊕M⊕M but not to M ⊕M. We also derive some relevant information about the endomorphism ring of M.

Original languageEnglish
Pages (from-to)1901-1907
Number of pages7
JournalProceedings of the American Mathematical Society
Volume126
Issue number7
DOIs
StatePublished - 1998
Externally publishedYes

Keywords

  • Endomorphism ring
  • Kaplansky test problems
  • Ni-separable group

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