Torsion classes generated by silting modules

Simion Breaz Babeş-Bolyai University Jan Žemlička Charles University in Prague

K-Theory and Homology mathscidoc:1912.43002

Arkiv for Matematik, 56, (1), 15-32, 2018
We study the classes of modules which are generated by a silting module. In the case of either hereditary or perfect rings, it is proved that these are exactly the torsion T such that the regular module has a special T-preenvelope. In particular, every torsion-enveloping class in Mod-R are of the form Gen(T) for a minimal silting module T. For the dual case, we obtain for general rings that the covering torsion-free classes of modules are exactly the classes of the form Cogen(T), where T is a cosilting module.
silting, precovering class, preenveloping class, torsion theory, cosilting
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@inproceedings{simion2018torsion,
  title={Torsion classes generated by silting modules},
  author={Simion Breaz, and Jan Žemlička},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191204091251657279558},
  booktitle={Arkiv for Matematik},
  volume={56},
  number={1},
  pages={15-32},
  year={2018},
}
Simion Breaz, and Jan Žemlička. Torsion classes generated by silting modules. 2018. Vol. 56. In Arkiv for Matematik. pp.15-32. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191204091251657279558.
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