Torsion classes generated by silting modules

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

Keywords

silting, precovering class, preenveloping class, torsion theory, cosilting

2010 Mathematics Subject Classification

16D90, 16E30, 18G15

Full Text (PDF format)

Received 2 May 2017

Received revised 28 July 2017

Accepted 9 August 2017

Published 30 April 2018