On radicals and products

Manfred Dugas and Rüdiger Göbel

Vol. 118 (1985), No. 1, 79–104

DOI: 10.2140/pjm.1985.118.79

Abstract

An Abelian group G is called cotorsion-free if 0 is the only pure-injective subgroup contained in G. If G is a cotorsion-free Abelian group, we construct a slender, ℵ₁-free Abelian group A such that Hom(A,G) = 0. This will be used to answer some questions about radicals and torsion theories of Abelian groups.

Mathematical Subject Classification 2000

Primary: 20K20

Secondary: 16A63

Milestones

Received: 22 November 1983

Revised: 22 February 1984

Published: 1 May 1985