Periodic Modules and Acyclic Complexes

Bazzoni, Silvana; Cortés Izurdiaga, Manuel; Estrada, Sergio

Publication:
Periodic Modules and Acyclic Complexes

dc.contributor.author	Bazzoni, Silvana
dc.contributor.author	Cortés Izurdiaga, Manuel
dc.contributor.author	Estrada, Sergio
dc.contributor.department	Matemáticas
dc.date.accessioned	2024-01-17T13:21:49Z
dc.date.available	2024-01-17T13:21:49Z
dc.date.issued	2019-08-07
dc.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	es
dc.description.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.	es
dc.format	application/pdf	es
dc.format.extent	20	es
dc.identifier.citation	Algebras and Representation Theory (2020) 23:1861–1883
dc.identifier.doi	https://doi.org/10.1007/s10468-019-09918-z
dc.identifier.issn	1572-9079
dc.identifier.issn	1386-923X
dc.identifier.uri	http://hdl.handle.net/10201/137402
dc.language	eng	es
dc.publisher	Springer	es
dc.relation	Sergio Estrada is partially supported by grants 18934/JLI/13 of Fundación Séneca- Agencia de Ciencia y Tecnología de la Región de Murcia in the framework of III PCTRM 2011- 2014, MTM2016-77445-P of Ministerio de Economía, Industria y Competitividad and FEDER funds.	es
dc.rights	info:eu-repo/semantics/openAccess	es
dc.rights	Attribution-NonCommercial-NoDerivatives 4.0 Internacional	*
dc.rights.uri	http://creativecommons.org/licenses/by-nc-nd/4.0/	*
dc.subject	Periodic C-module	es
dc.subject	Pure C-periodic module	es
dc.subject	Locally split short exact sequence	es
dc.subject	Hereditary cotorsion pair	es
dc.subject	Acyclic complex	es
dc.subject.other	CDU::5 - Ciencias puras y naturales	es
dc.title	Periodic Modules and Acyclic Complexes	es
dc.type	info:eu-repo/semantics/article	es
dspace.entity.type	Publication	es