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...
| Autores: | ; |
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| Tipo de documento: | Artigo |
| Data de publicação: | 2008 |
| País: | España |
| Recursos: | Universitat Autònoma de Barcelona |
| Repositório: | Dipòsit Digital de Documents de la UAB |
| Idioma: | Inglês |
| OAI Identifier: | oai:ddd.uab.cat:115171 |
| Acesso em linha: | https://ddd.uab.cat/record/115171 https://dx.doi.org/urn:doi:10.1512/iumj.2008.57.3325 |
| Nível de acesso: | Acesso aberto |
| Palavra-chave: | Mittag-Leffler inverse system Cotorsion pairs Tilting modules Baer |
| Resumo: | 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. |
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