Arkiv för Matematik

Torsion classes generated by silting modules

Simion Breaz and Jan Žemlička

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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.

Article information

Source
Ark. Mat., Volume 56, Number 1 (2018), 15-32.

Dates
Received: 2 May 2017
Revised: 28 July 2017
First available in Project Euclid: 19 June 2019

Permanent link to this document
https://projecteuclid.org/euclid.afm/1560967217

Digital Object Identifier
doi:10.4310/ARKIV.2018.v56.n1.a2

Mathematical Reviews number (MathSciNet)
MR3800456

Zentralblatt MATH identifier
06869099

Subjects
Primary: 16D90: Module categories [See also 16Gxx, 16S90]; module theory in a category-theoretic context; Morita equivalence and duality 16E30: Homological functors on modules (Tor, Ext, etc.) 18G15: Ext and Tor, generalizations, Künneth formula [See also 55U25]

Keywords
silting precovering class preenveloping class torsion theory cosilting

Citation

Breaz, Simion; Žemlička, Jan. Torsion classes generated by silting modules. Ark. Mat. 56 (2018), no. 1, 15--32. doi:10.4310/ARKIV.2018.v56.n1.a2. https://projecteuclid.org/euclid.afm/1560967217


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