Cotorsion theories and splitters

Rüdiger Göbel*, Saharon Shelah

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

39 Scopus citations

Abstract

Let A be a subring of the rationals. We want to investigate self splitting fi-modules G (that is ExtR(G,G) = 0). Following Schultz, we call such modules splitters. Free modules and torsion-free cotorsion modules are classical examples of splitters. Are there others? Answering an open problem posed by Schultz, we will show that there are more splitters, in fact we are able to prescribe their endomorphism H-algebras with a free Ä-module structure. As a by-product we are able to solve a problem of Sake, showing that all rational cotorsion theories have enough injectives and enough projectives. This is also basic for answering the flat-cover-conjecture.

Original languageEnglish
Pages (from-to)5357-5379
Number of pages23
JournalTransactions of the American Mathematical Society
Volume352
Issue number11
DOIs
StatePublished - 2000
Externally publishedYes

Keywords

  • Completions
  • Cotorsion theories
  • Enough pro-jectives
  • Realizing rings as endomorphism rings of self-splitting modules
  • Self-splitting modules

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