On the existence of rigid aleph₁-free abelian groups of cardinality aleph₁

2001/04/19 by Rüdiger Göbel, Saharon Shelah
Mathematics · #math.LO #math.GR

paper · pdf

published as 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

arxiv created 2001/04/19 · arxiv updated 2009/11/30

Abstract

An abelian group is said to be aleph₁-free if all its countable subgroups are free. Our main result is: If R is a ring with R⁺ free and |R|<lambda <= 2^aleph₀, then there exists an aleph₁-free abelian group G of cardinality lambda with End(G)=R . A corollary to this theorem is: Indecomposable aleph₁-free abelian groups of cardinality aleph₁ do exist.

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