Finiteness criteria for Gorenstein homological dimension and some invariants of groups

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.

arXiv comment19 pages

References in corpus (6)

• Singular compactness and definability for $\Sigma$-cotorsion and Gorenstein modules
• Periodic modules and acyclic complexes
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• Finiteness criteria for Gorenstein flat dimension and stability
• Gorenstein modules and dimension over large families of infinite groups
• Gorenstein homological dimension and some invariants of groups

Cited by in corpus (1)

• Gorenstein analogues of a projectivity criterion over group algebras