# Sh:647

• Göbel, R., & Shelah, S. (2000). Cotorsion theories and splitters. Trans. Amer. Math. Soc., 352(11), 5357–5379.
• Abstract:
Let R be a subring of the rationals. We want to investigate self splitting R-modules G that is {\rm 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.
• published version (23p)
Bib entry
@article{Sh:647,
author = {G{\"o}bel, R{\"u}diger and Shelah, Saharon},
title = {{Cotorsion theories and splitters}},
journal = {Trans. Amer. Math. Soc.},
fjournal = {Transactions of the American Mathematical Society},
volume = {352},
number = {11},
year = {2000},
pages = {5357--5379},
issn = {0002-9947},
doi = {10.1090/S0002-9947-00-02475-2},
mrclass = {20K35 (20K20 20K40)},
mrnumber = {1661246},
mrreviewer = {Luigi Salce},
doi = {10.1090/S0002-9947-00-02475-2},
note = {\href{https://arxiv.org/abs/math/9910159}{arXiv: math/9910159}},
arxiv_number = {math/9910159},
keyword = {cotorsion theories, completions, self-splitting modules, enough
projectives, realizing rings as endomorphism rings of self-splitting
modules}
}