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Recollements of Module Categories

Abstract

We establish a correspondence between recollements of abelian categories up to equivalence and certain TTF-triples. For a module category we show, moreover, a correspondence with idempotent ideals, recovering a theorem of Jans. Furthermore, we show that a recollement whose terms are module categories is equivalent to one induced by an idempotent element, thus answering a question by Kuhn.

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Correspondence to Chrysostomos Psaroudakis.

Additional information

The first named author is co-funded by the European Union—European Social Fund (ESF) and National Sources, in the framework of the program “HRAKLEITOS II” of the “Operational Program Education and Life Long Learning” of the Hellenic Ministry of Education, Life Long Learning and religious affairs. The second named author was supported by DFG-SPP 1388, at the University of Stuttgart, for most of this project. This work was completed during a visit of the second author to the SFB 701 in Bielefeld.

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Psaroudakis, C., Vitória, J. Recollements of Module Categories. Appl Categor Struct 22, 579–593 (2014). https://doi.org/10.1007/s10485-013-9323-x

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  • DOI: https://doi.org/10.1007/s10485-013-9323-x

Keywords

  • Recollement
  • TTF-triple
  • Idempotent ideal
  • Ring epimorphism

Mathematics Subject Classifications (2010)

  • 18E35
  • 18E40
  • 16S90