Subgroups of the Baer-Specker Group with Few Endomorphisms but Large Dual

Andreas Blass; Rüdiger Göbel

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Subgroups of the Baer-Specker Group with Few Endomorphisms but Large Dual

Andreas Blass·Rüdiger Göbel

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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.

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BibTeX RIS

Andreas Blass, Rüdiger Göbel. 1994-05-23. Subgroups of the Baer-Specker Group with Few Endomorphisms but Large Dual. https://arxiv.org/abs/math/9405206

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