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 language | English |
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Pages (from-to) | 1901-1907 |
Number of pages | 7 |
Journal | Proceedings of the American Mathematical Society |
Volume | 126 |
Issue number | 7 |
DOIs | |
State | Published - 1998 |
Externally published | Yes |
Keywords
- Endomorphism ring
- Kaplansky test problems
- Ni-separable group