Finiteness criteria for Gorenstein homological dimension and some invariants of groups
arXiv:2311.02768 · doi:10.1080/00927872.2025.2465908
Abstract
In this paper, we study finiteness criteria for the Gorenstein homological dimension of groups over a commutative ring of finite Gorenstein weak global dimension and provide estimates for the Gorenstein weak global dimension of group rings. As a result, we obtain Gorenstein analogues of well known properties in classical homological algebra over large families of infinite groups. Moreover, we prove that over a commutative ring of finite Gorenstein weak global dimension, the Gorenstein cohomological dimension of a group G bounds its Gorenstein homological dimension. Finally, we compare the generalized cohomological dimension and the generalized homological dimension of a group.
19 pages