Subgroups of the Baer–Specker group with few endomorphisms but large dual

Andreas Blass; Rüdiger Göbel

Fundamenta Mathematicae (1996)

  • Volume: 149, Issue: 1, page 19-29
  • ISSN: 0016-2736

Abstract

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Assuming the continuum hypothesis, we construct a pure subgroup G of the Baer-Specker group ℤ ℵ 0 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.

How to cite

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Blass, Andreas, and Göbel, Rüdiger. "Subgroups of the Baer–Specker group with few endomorphisms but large dual." Fundamenta Mathematicae 149.1 (1996): 19-29. <http://eudml.org/doc/212105>.

@article{Blass1996,
abstract = {Assuming the continuum hypothesis, we construct a pure subgroup G of the Baer-Specker group $ℤ^\{ℵ_0\}$ 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.},
author = {Blass, Andreas, Göbel, Rüdiger},
journal = {Fundamenta Mathematicae},
keywords = {dual groups; endomorphism rings; endomorphisms of finite rank; subgroups of finite rank; pure subgroups; direct summands},
language = {eng},
number = {1},
pages = {19-29},
title = {Subgroups of the Baer–Specker group with few endomorphisms but large dual},
url = {http://eudml.org/doc/212105},
volume = {149},
year = {1996},
}

TY - JOUR
AU - Blass, Andreas
AU - Göbel, Rüdiger
TI - Subgroups of the Baer–Specker group with few endomorphisms but large dual
JO - Fundamenta Mathematicae
PY - 1996
VL - 149
IS - 1
SP - 19
EP - 29
AB - Assuming the continuum hypothesis, we construct a pure subgroup G of the Baer-Specker group $ℤ^{ℵ_0}$ 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.
LA - eng
KW - dual groups; endomorphism rings; endomorphisms of finite rank; subgroups of finite rank; pure subgroups; direct summands
UR - http://eudml.org/doc/212105
ER -

References

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