A class of torsion-free abelian groups characterized by the ranks of their socles. (English) Zbl 1013.13007

Summary: Butler groups formed by factoring a completely decomposable group by a rank one group have been studied extensively. We call such groups bracket groups. We study bracket modules over integral domains. In particular, we are interested in when any bracket \(R\)-module is \(R\) tensor a bracket group.


13C13 Other special types of modules and ideals in commutative rings
20K15 Torsion-free groups, finite rank
13G05 Integral domains
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