Mittag-Leffler conditions on modules
Rings and Algebras
2007-05-23 v1 K-Theory and Homology
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.
Cite
@article{arxiv.0704.3690,
title = {Mittag-Leffler conditions on modules},
author = {Lidia Angeleri-Hugel and Dolors Herbera},
journal= {arXiv preprint arXiv:0704.3690},
year = {2007}
}