Mittag-Leffler conditions on modules

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...

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Detalles Bibliográficos
Autores: Angeleri Hügel, Lidia, Herbera i Espinal, Dolors|||0000-0002-2350-7248
Tipo de recurso: artículo
Fecha de publicación:2008
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:115171
Acceso en línea:https://ddd.uab.cat/record/115171
https://dx.doi.org/urn:doi:10.1512/iumj.2008.57.3325
Access Level:acceso abierto
Palabra clave:Mittag-Leffler inverse system
Cotorsion pairs
Tilting modules
Baer
Descripción
Sumario: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.