Cotorsion Theories and Splitters
逻辑
2007-05-23 v1 交换代数
环与代数
摘要
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.
引用
@article{arxiv.math/9910159,
title = {Cotorsion Theories and Splitters},
author = {Ruediger Goebel and Saharon Shelah},
journal= {arXiv preprint arXiv:math/9910159},
year = {2007}
}