### Endomorphism Rings of Modules whose cardinality is cofinal to $\omega$

by Goebel and Shelah. [GbSh:547]

Abelian groups, module theory, and topology (Padua, 1997), 1998

The main result is
Theorem: Let A be an R-algebra, mu, lambda be cardinals such
that |A| <= mu = mu^{aleph_0}< lambda <= 2^mu . If A is
aleph_0-cotorsion-free or A is countably free, respectively,
then there exists an aleph_0-cotorsion-free or a separable
(reduced, torsion-free) R-module G respectively of cardinality
|G|= lambda with End_R G=A oplus Fin G .

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