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

Lars Winther Christensen; Sergio Estrada; Li Liang; Peder Thompson; Dejun Wu; Gang Yang

doi:10.1016/j.jalgebra.2020.09.024

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

Lars Winther Christensen, Sergio Estrada, Li Liang, Peder Thompson, Dejun Wu, Gang Yang

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

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 dimension 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.

Original language	English
Pages (from-to)	346-370
Number of pages	25
Journal	Journal of Algebra
Volume	567
DOIs	https://doi.org/10.1016/j.jalgebra.2020.09.024
State	Published - Feb 1 2021

Keywords

Flat-cotorsion module
Gorenstein flat dimension
Gorenstein flat-cotorsion dimension

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10.1016/j.jalgebra.2020.09.024

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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 dimension 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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AU - Christensen, Lars Winther

AU - Estrada, Sergio

AU - Liang, Li

AU - Thompson, Peder

AU - Wu, Dejun

AU - Yang, Gang

PY - 2021/2/1

Y1 - 2021/2/1

N2 - 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 dimension 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.

AB - 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 dimension 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.

KW - Flat-cotorsion module

KW - Gorenstein flat dimension

KW - Gorenstein flat-cotorsion dimension

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JO - Journal of Algebra

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