The kaplansky test problems for ni-separable groups

Paul C. Eklof; Saharon Shelah

doi:10.1090/s0002-9939-98-04749-2

The kaplansky test problems for ni-separable groups

Paul C. Eklof^*, Saharon Shelah

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-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 language	English
Pages (from-to)	1901-1907
Number of pages	7
Journal	Proceedings of the American Mathematical Society
Volume	126
Issue number	7
DOIs	https://doi.org/10.1090/s0002-9939-98-04749-2
State	Published - 1998
Externally published	Yes

Keywords

Endomorphism ring
Kaplansky test problems
Ni-separable group

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10.1090/s0002-9939-98-04749-2

Cite this

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AB - 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.

KW - Endomorphism ring

KW - Kaplansky test problems

KW - Ni-separable group

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The kaplansky test problems for ni-separable groups

Abstract

Keywords

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