Abstract
We study Mittag-Leffler conditions on modules providing relative versions of classical results by Raynaud and Gruson. We then apply our investigations to several contexts. First of all, we give a new argument for solving the Baer splitting problem. Moreover, we show that modules arising in cotorsion pairs satisfy certain Mittag-Leffler conditions. In particular, this implies that tilting modules satisfy a useful finiteness condition over their endomorphism ring. In the final section, we focus on a special tilting cotorsion pair related to the pure-semisimplicity conjecture.
Original language | English |
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Pages (from-to) | 2459-2517 |
Journal | Indiana University Mathematics Journal |
Volume | 57 |
DOIs | |
Publication status | Published - 16 Dec 2008 |
Keywords
- Baer modules
- Cotorsion pairs
- Mittag-Leffler inverse system
- Pure semisimple rings
- Tilting modules