Publication: Periodic Modules and Acyclic Complexes
Authors
Bazzoni, Silvana ; Cortés Izurdiaga, Manuel ; Estrada, Sergio
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Publisher
Springer
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DOI
https://doi.org/10.1007/s10468-019-09918-z
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info:eu-repo/semantics/article
Description
©2019. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
This document is the Accepted version of a Published Work that appeared in final form in https://doi.org/10.1007/s10468-019-09918-z. To access the final edited and published work see https://doi.org/10.1007/s10468-019-09918-z
Abstract
We study the behaviour of modules M that fit into a short exact sequence 0 → M → C →
M → 0, where C belongs to a class of modules C, the so-called C-periodic modules. We
find a rather general framework to improve and generalize some well-known results of Benson
and Goodearl and Simson. In the second part we will combine techniques of hereditary
cotorsion pairs and presentation of direct limits, to conclude, among other applications, that
if M is any module and C is cotorsion, then M will be also cotorsion. This will lead to some
meaningful consequences in the category Ch(R) of unbounded chain complexes and in
Gorenstein homological algebra. For example we show that every acyclic complex of cotorsion
modules has cotorsion cycles, and more generally, every map F → C where C is a
complex of cotorsion modules and F is an acyclic complex of flat cycles, is null-homotopic.
In other words, every complex of cotorsion modules is dg-cotorsion.
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Citation
Algebras and Representation Theory (2020) 23:1861–1883
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