2007/04/27 by Lidia Angeleri Hügel, Lidia Angeleri-Hugel, Angeleri-Hugel, Lidia +2
Mathematics · Physics and Astronomy · #16D70 #16L30 #18E15 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #K-Theory and Homology (math.KT) #Nonlinear Waves and Solitons #Rings and Algebras (math.RA) #math.KT #math.RA #msc:16D70 #msc:16L30 #msc:18E15
paper · pdf · doi:10.48550/arxiv.0704.3690
45 pages
arxiv created 2007/04/27 · openalex publication_date 2007/04/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.