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

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. (C) 2020 Elsevier Inc. All rights reserved.

Automated summary

We introduce a refinement of the Gorenstein flat dimension for complexes over associative rings, called the Gorenstein flat-cotorsion dimension, which behaves like a homological dimension without extra assumptions. It coincides with the Gorenstein flat dimension for finite complexes and for complexes over right coherent rings.