Self-splitting Abelian groups (Q2748268)

This paper was written in 1988 and widely circulated as Research Report of the University of Western Australia. It stimulated research, particularly in the last half decade which finally also lead to the solution of the flat cover conjecture. The paper deals with the question which Abelian groups \(G\) (here for the first time called splitters) are of the form \(\text{Ext}(G,G)=0\). Classical results of splitters, like the reduction to the case of uncountable, torsion-free, reduced Abelian groups \(G\) are derived in this paper. Important results on \(\bigoplus\)-splitters (\(\prod\)-splitters) satisfying \(\text{Ext}(\bigoplus G,\bigoplus G)=0\) (\(\text{Ext}(\prod G,\prod G)=0)\) can be looked up here. The connection to cover problems became clear in conjunction with \textit{L. Salce}'s paper [in Symp. Math. 23, 11-32 (1979; Zbl 0426.20044)]. In Section 6 the author also discusses some of the new developments. It is good to see this manuscript finally, after 13 years, being published.