Mittag-Leffler conditions on modules

Lidia Angeleri Hügel, Dolors Herbera

Research output: Contribution to journalArticleResearchpeer-review

39 Citations (Scopus)

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 languageEnglish
Pages (from-to)2459-2517
JournalIndiana University Mathematics Journal
Volume57
DOIs
Publication statusPublished - 16 Dec 2008

Keywords

  • Baer modules
  • Cotorsion pairs
  • Mittag-Leffler inverse system
  • Pure semisimple rings
  • Tilting modules

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