Publication:
A refinement of Gorenstein flat dimension via the flat–cotorsion theory

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Date
2021-02-01
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Authors
Christensen, Lars Winther ; Estrada, Sergio ; Liang, Li ; Thompson, Peder ; Wu, Dejun ; Yang, Gang
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Publisher
ScienceDirect
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Matemáticas
DOI
https://doi.org/10.1016/j.jalgebra.2020.09.024
0021-8693
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info:eu-repo/semantics/article
Description
©2021. 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 Journal of Algebra. To access the final edited and published work see https://doi.org/10.1016/j.jalgebra.2020.09.024
Abstract
We introduce a refinement of the Gorenstein flat dimension for complexes over an associative ring—the Gorenstein flat-cotorsion dimension—and prove that it, unlike the Gorenstein flat dimension, behaves as one expects of a homological di-mension without extra assumptions on the ring. Crucially, we show that it coincides with the Gorenstein flat dimension for complexes where the latter is finite, and for complexes over right coherent rings—the setting where the Gorenstein flat dimension is known to behave as expected.
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Flat-cotorsion module , Gorenstein flat dimension , Gorenstein flat-cotorsion dimension
Citation
Journal of Algebra
URI
http://hdl.handle.net/10201/137422
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