The groups \(N^ rK_ 0(\mathbb{Z}\pi )\) are finitely generated \(\mathbb{Z} [\mathbb{N}^ r]\)-modules if \(\pi\) is a finite group
type: Item
instance of: scholarly article
title: The groups \(N^ rK_ 0(\mathbb{Z}\pi )\) are finitely generated \(\mathbb{Z} [\mathbb{N}^ r]\)-modules if \(\pi\) is a finite group
zbMATH Open document ID: 0829.19001
DOI: 10.1007/BF00965456
author: Francis Connolly
author: Marío O. M. Da Silva
published in: \(K\)-Theory
publication date: 1996-01-17T00:00:00Z
review text: For any ring \(R\), any integer \(i \leq 1\) and any integer \(r \geq 0\), the \(K\)-theory nil group, \(N^r K_i (R)\) is either zero or non-finitely generated as a \(\mathbb{Z}\)-module. In this paper the authors observe that \(N^r K_i(R)\) admits a \(\mathbb{Z} [\mathbb{N}^r]\)-module structure where \(\mathbb{N}\) is the multiplicative monoid of positive integers. They then prove that, for any finite group \(\pi\), the nil group \(N^r K_i (\mathbb{Z} [\pi])\) is finitely generated as a \(\mathbb{Z} [\mathbb{N}^r]\)- module. Moreover, they exhibit a power of the order of \(\pi\) which annihilates \(N^r K_i(\mathbb{Z} [\pi])\). The methods of the paper are strictly algebraic.
reviewed by: Hans Jørgen Munkholm
Mathematics Subject Classification ID: 19D35
zbMATH DE Number: 784411
zbMATH Keywords: nil \(K\)-theory
zbMATH Keywords: finitely generated
zbMATH Keywords: monoid algebra
zbMATH Keywords: group algebra
zbMATH Keywords: Verschiebung
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00965456
OpenAlex ID: W2319046334
description: scientific article; zbMATH DE number 784411