Homologically trivial actions on chain complexes and finiteness properties of infinite groups
type: Item
instance of: scholarly article
title: Homologically trivial actions on chain complexes and finiteness properties of infinite groups
zbMATH Open document ID: 0822.13006
DOI: 10.1016/0022-4049(94)90034-5
published in: Journal of Pure and Applied Algebra
publication date: 1994-08-07T00:00:00Z
review text: The author uses the technique for grafting together finite chain complexes with the homology of a sphere introduced by \textit{R. G. Swan} [Ann. Math. (2) 72, 267--291 (1960; Zbl 0096.01701)] to prove the following result: Let \(G\) be a group and \(R\) a commutative Noetherian ring. Then \(R\) as trivial \(G\)-module has an \(RG\)-projective resolution by finitely generated modules \((: G\) is of type \(FP (\infty, R))\) if and only if there is an \(R\)-augmented chain complex of finitely generated projective \(RG\)-modules such that the homology groups are finitely generated over \(R\) and trivial over \(G\).
Mathematics Subject Classification ID: 13D03
Mathematics Subject Classification ID: 13D02
Mathematics Subject Classification ID: 55U15
zbMATH DE Number: 612148
zbMATH Keywords: grafting chain complexes
zbMATH Keywords: projective resolution
author: Christopher W. Stark
MaRDI profile type: Publication
full work available at URL: 0022-4049(94)90034-5
OpenAlex ID: W1995399334
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description: scientific article; zbMATH DE number 612148