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

Fundamenta Mathematicae (1996)

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

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topBlass, 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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- [9] M. Dugas und R. Göbel, Endomorphism rings of separable torsion-free abelian groups, Houston J. Math 11 (1985), 471-483. Zbl0597.20046
- [10] M. Dugas and J. Irwin, On basic subgroups of Π Z, Comm. Algebra 19 (1991), 2907-2921. Zbl0753.20015
- [11] M. Dugas and J. Irwin, On pure subgroups of cartesian products of integers, Resultate Math. 15 (1989), 35-52. Zbl0671.20052
- [12] M. Dugas, J. Irwin and S. Khabbaz, Countable rings as endomorphism rings, Quart. J. Math. Oxford 39 (1988), 201-211. Zbl0663.20058
- [13] K. Eda, A note on subgroups of ${\mathbb{Z}}^{\mathbb{N}}$, in: Abelian Group Theory, R. Göbel, L. Lady and A. Mader (eds.), Lecture Notes in Math. 1006, Springer, 1983, 371-374.

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