## Cotorsion theories and splitters (2000)

Citations: | 10 - 6 self |

### BibTeX

@MISC{Göbel00cotorsiontheories,

author = {Rüdiger Göbel and Saharon Shelah},

title = {Cotorsion theories and splitters},

year = {2000}

}

### OpenURL

### Abstract

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. 647 revision:1999-10-26 modified:1999-10-26 1