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arXiv:math/0104194 [math.LO]AbstractReferencesReviewsResources

On the existence of rigid aleph_1-free abelian groups of cardinality aleph_1

Rüdiger Göbel, Saharon Shelah

Published 2001-04-19Version 1

An abelian group is said to be aleph_1-free if all its countable subgroups are free. Our main result is: If R is a ring with R^+ free and |R|<lambda <= 2^{aleph_0}, then there exists an aleph_1-free abelian group G of cardinality lambda with End(G)=R . A corollary to this theorem is: Indecomposable aleph_1-free abelian groups of cardinality aleph_1 do exist.

Journal: Abelian Groups and Modules. Proceedings of the Padova Conference, Padova, Italy, 1994. Editors: A. Facchini and C. Menini. Kluwer, New York, 1995, pp 227--237
Categories: math.LO, math.GR
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