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

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dc.creatorGöbel, Rüdiger
dc.creatorShelah, Saharon
dc.date2001-04-19
dc.date.accessioned2026-07-07T04:41:23Z
dc.date.available2026-07-07T04:41:23Z
dc.descriptionAn 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.
dc.identifierhttps://arxiv.org/abs/math/0104194
dc.identifierhttp://arxiv.org/abs/math/0104194
dc.identifierAbelian Groups and Modules. Proceedings of the Padova Conference, Padova, Italy, 1994. Editors: A. Facchini and C. Menini. Kluwer, New York, 1995, pp 227--237
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/61335
dc.subjectLogic
dc.subjectGroup Theory
dc.titleOn the existence of rigid aleph_1-free abelian groups of cardinality aleph_1
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