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

Rüdiger Göbel; Saharon Shelah

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

Rüdiger Göbel·Saharon Shelah

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Abstract

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.

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BibTeX RIS

Rüdiger Göbel, Saharon Shelah. 2001-04-19. On the existence of rigid aleph_1-free abelian groups of cardinality aleph_1. https://arxiv.org/abs/math/0104194

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