Vol. 47, No. 1, 1973

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The structure of ultraproducts of abelian groups

Paul C. Eklof

Vol. 47 (1973), No. 1, 67–79
Abstract

A structure theorem is given which characterizes abelian groups which are ultrapowers with respect to ω-incomplete ultrafilters. It is also proved that any nonprincipal ultraproduct of abelian groups over a countable index set—or, more generally, with respect to a good ultrafilter—is an ultrapower with respect to an ω-incomplete ultrafilter. The results of this paper provide a solution to a problem of L. Fuchs.

Mathematical Subject Classification 2000
Primary: 20K25
Milestones
Received: 18 April 1972
Published: 1 July 1973
Authors
Paul C. Eklof