Finiteness criteria for Gorenstein homological dimension and some invariants of groups

Fuente: arXiv
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Autori principali: Kaperonis, Ilias, Stergiopoulou, Dimitra-Dionysia
Natura: Preprint
Pubblicazione: 2023
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author Kaperonis, Ilias
Stergiopoulou, Dimitra-Dionysia
author_facet Kaperonis, Ilias
Stergiopoulou, Dimitra-Dionysia
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2311_02768
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Finiteness criteria for Gorenstein homological dimension and some invariants of groups
Kaperonis, Ilias
Stergiopoulou, Dimitra-Dionysia
Commutative Algebra
Rings and Algebras
18G20
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.
title Finiteness criteria for Gorenstein homological dimension and some invariants of groups
topic Commutative Algebra
Rings and Algebras
18G20
url https://arxiv.org/abs/2311.02768