English

Torsion classes generated by silting modules

Representation Theory 2017-04-06 v3 Rings and Algebras

Abstract

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\mathcal{T} such that the regular module has a special T\mathcal{T}-preenvelope. In particular every torsion enveloping class in Mod-R\textrm{Mod-} R are of the form Gen(T)\mathrm{Gen}(T) for a minimal silting module TT. 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)\mathrm{Cogen}(T), where TT is a cosilting module.

Keywords

Cite

@article{arxiv.1601.06655,
  title  = {Torsion classes generated by silting modules},
  author = {Simion Breaz and Jan Žemlička},
  journal= {arXiv preprint arXiv:1601.06655},
  year   = {2017}
}

Comments

Preliminary version; comments are welcome; v2: improved version; an important gap in the initial version was completed; v3: We added some examples; references added and updated

R2 v1 2026-06-22T12:36:08.830Z