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Faithful Abelian groups of infinite rank. (English) Zbl 0646.20042
Let A be a torsion-free abelian group. The author finds necessary and sufficient conditions on a torsion-free abelian group G for every epimorphism of G onto a summand of a direct sum of copies of A to split. This result is a generalization of well-known theorems of Baer and Arnold-Lady. Several examples and applications are also described.
Reviewer: P.Schultz

MSC:
20K20 Torsion-free groups, infinite rank
20K30 Automorphisms, homomorphisms, endomorphisms, etc. for abelian groups
16S50 Endomorphism rings; matrix rings
20K25 Direct sums, direct products, etc. for abelian groups
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