Vol. 50, No. 2, 1974

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A class of Abelian groups closed under direct limits and subgroups formation

Chin-Shui Hsu

Vol. 50 (1974), No. 2, 495–503

This is a solution to the following problem: Which classes of Abelian groups are closed under taking subgroups and direct limits. (Problem 6(a), L. Fuchs, Infinite Abelian Groups, I, A-P.) Each such class is uniquely determined by its subclass of finitely generated Abelian groups, which in turn can be described by a set of numerical invariants.

In like manner, an analogue for modules over a Dedekind domain is also obtained.

Mathematical Subject Classification
Primary: 20K05
Received: 31 December 1970
Published: 1 February 1974
Chin-Shui Hsu