Subgroups of the Baer-Specker Group with Few Endomorphisms but Large Dual
Abstract
The Baer-Specker group is the product of countably many copies of the additive group Z of integers. Assuming the continuum hypothesis, we construct a pure subgroup G of the Baer-Specker group with the following properties. Every endomorphism of G differs from a scalar multiplication by an endomorphism of finite rank. Yet G has uncountably many homomorphisms to Z.
- Publication:
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arXiv Mathematics e-prints
- Pub Date:
- May 1994
- DOI:
- 10.48550/arXiv.math/9405206
- arXiv:
- arXiv:math/9405206
- Bibcode:
- 1994math......5206B
- Keywords:
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- Mathematics - Logic