COTORSION THEORIES AND SPLITTERS

Let R be a subring of the rationals. We want to investigate self splitting R-modules G that is Ext R(G; G) = 0 holds and follow Schultz [22] to call such modules splitters. Free modules and torsion-free cotorsion modules are classical examples for splitters. Are there others? Answering an open problem by Schultz [22] we will show that there are more splitters, in fact we are able to prescribe their endomorphism R-algebras with a free R-module structure. As a byproduct we are able to answer a problem of Salce [21] showing that all rational cotorsion theories have enough injectives and enough projectives.