On the existence of rigid aleph₁-free abelian groups of cardinality aleph₁
Göbel, Rüdiger · Shelah, Saharon
Original · EN
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 <= 2aleph₀, 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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