1999/10/28 by Ruediger Goebel, Saharon Shelah, Goebel, Ruediger +1
Mathematics · #13D30 #18E40 #18G05 #20K20 #20K35 #20K40 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics #Logic (math.LO) #Rings and Algebras (math.RA) #Rings, Modules, and Algebras #math.AC #math.LO #math.RA #msc:13D30 #msc:18E40 #msc:18G05 #msc:20K20 #msc:20K35 #msc:20K40
paper · pdf · doi:10.48550/arxiv.math/9910159
published as Trans. Amer. Math. Soc. 352 No. 11 (2000) 5357--5379
arxiv created 1999/10/28 · openalex publication_date 1999/10/28 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let R be a subring of the rationals. We want to investigate self splitting R-modules G that is ExtR(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.