On Gorenstein global and Gorenstein weak global dimensions
Volume 174 / 2023
Colloquium Mathematicum 174 (2023), 45-67
MSC: Primary 18G25; Secondary 16E65, 18G20.
DOI: 10.4064/cm9052-7-2023
Published online: 28 September 2023
Abstract
It is well-known that the weak global dimension of a ring does not exceed its global dimension. Christensen et al. obtained a corresponding result in Gorenstein setting for coherent rings. We extend this result to an arbitrary ring. As applications, we characterize the finiteness of (Gorenstein) global dimension by singularity categories and Gorenstein flat modules.