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

Chin-Shui Hsu

Vol. 50 (1974), No. 2, 495–503

DOI: 10.2140/pjm.1974.50.495

Abstract

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

Milestones

Received: 31 December 1970

Published: 1 February 1974