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arXiv · 2311.02768

Finiteness criteria for Gorenstein homological dimension and some invariants of groups

Ilias Kaperonis·Dimitra-Dionysia Stergiopoulou
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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.

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Ilias Kaperonis, Dimitra-Dionysia Stergiopoulou. 2023-11-05. Finiteness criteria for Gorenstein homological dimension and some invariants of groups. https://doi.org/10.1080/00927872.2025.2465908

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