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# Arkiv för Matematik

## Volume 56 (2018)

### Number 1

### Torsion classes generated by silting modules

Pages: 15 – 32

DOI: https://dx.doi.org/10.4310/ARKIV.2018.v56.n1.a2

#### Authors

#### 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 $\mathcal{T}$ 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

Received 2 May 2017

Received revised 28 July 2017

Accepted 9 August 2017

Published 30 April 2018