A refinement of Gorenstein flat dimension via the flat--cotorsion theory
Peer reviewed, Journal article
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Date
2021Metadata
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- Institutt for matematiske fag [2354]
- Publikasjoner fra CRIStin - NTNU [37257]
Original version
Journal of Algebra. 2021, 567, 346-370. https://doi.org/10.1016/j.jalgebra.2020.09.024Abstract
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.