### Cotorsion theories and splitters

by Goebel and Shelah. [GbSh:647]

Transactions American Math Soc, 2000

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 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 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
showing that all rational cotorsion theories have enough injectives
and enough projectives.

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