### On the existence of rigid $\aleph_1$-free abelian groups of cardinality $\aleph_1$

by Goebel and Shelah. [GbSh:519]

Abelian Groups and Modules, 1995

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.

Back to the list of publications