Mittag-Leffler conditions on modules

By Lidia Angeleri-Hugel, Dolors Herbera. 2007

68 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/596d4d97d066f131d204ce3ca4ae9e99874377e2

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In Algebra and Number Theory

In Geometry and Topology

In Statistical and Nonlinear Physics

Citations in the corpus

Almost free modules and Mittag-Leffler conditions (2009, background): “Mittag–Leffler and relative Mittag–Leffler modules were studied in depth in [29] and [1], respectively.”
Good tilting modules and recollements of derived module categories (2010, methodology): “Now, we recall the definition of Mittag-Leffler modules (see [20, 3]).”