Flat modules over group rings of finite groups
type: Item
instance of: scholarly article
title: Flat modules over group rings of finite groups
zbMATH Open document ID: 0938.20003
DOI: 10.1023/A:1009918813260
published in: Algebras and Representation Theory
publication date: 2000-03-21T00:00:00Z
review text: Let \(kG\) be the group ring of a finite group \(G\) over a commutative ring \(k\). The author studies the question of existence of a flat \(kG\)-module \(M\) which is projective as \(k\)-module but \(M\) is not projective as \(kG\)-module. He relates this question to the question of existence of a \(k\)-module which is flat and periodic but not projective. For either question to have a positive answer, it is at least necessary to have \(|k|\geq\aleph_\omega\). Moreover, he proves that there can be no such example if \(k\) is a commutative Noetherian ring with finite Krull dimension, or if \(k\) is a perfect ring.
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 16D40
Mathematics Subject Classification ID: 16S34
zbMATH DE Number: 1385254
zbMATH Keywords: flat modules
zbMATH Keywords: projective modules
zbMATH Keywords: group rings
zbMATH Keywords: finite groups
author: David Benson
reviewed by: S. V. Mihovski
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1385254