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 language | English |
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Pages (from-to) | 5357-5379 |
Number of pages | 23 |
Journal | Transactions of the American Mathematical Society |
Volume | 352 |
Issue number | 11 |
DOIs | |
State | Published - 2000 |
Externally published | Yes |
Keywords
- Completions
- Cotorsion theories
- Enough pro-jectives
- Realizing rings as endomorphism rings of self-splitting modules
- Self-splitting modules