Lie ideals in group rings
type: Item
instance of: scholarly article
title: Lie ideals in group rings
zbMATH Open document ID: 0689.16005
DOI: 10.1016/0022-4049(90)90056-N
author: J. B. Srivastava
author: Rajendra Kumar Sharma
published in: Journal of Pure and Applied Algebra
publication date: 1990-01-01T00:00:00Z
review text: Let U be a Lie ideal of the associative ring R and suppose that U is Lie nilpotent of class \(n\geq 3\). Then it is shown that \(\gamma_ 3(U)R\) is a nilpotent ideal of index at most 2n-4. Next, if R is a Lie nilpotent algebra of characteristic \(p>0\), then the Lie commutators generate a nil ideal of bounded exponent. Finally, let \(R=K[G]\) be the group algebra of the group G over the field K of characteristic \(p\geq 0\) and assume that R is Lie nilpotent of class less than n. If \(p=0\) or \(p\geq n\), then G is abelian. On the other hand, if \(p<n\) then G is nilpotent of class bounded by a function of n and p.
Mathematics Subject Classification ID: 16S34
Mathematics Subject Classification ID: 16W10
Mathematics Subject Classification ID: 16N40
Mathematics Subject Classification ID: 20F18
zbMATH DE Number: 4129005
zbMATH Keywords: Lie ideal
zbMATH Keywords: Lie nilpotent algebra
zbMATH Keywords: Lie commutators
zbMATH Keywords: nil ideal of bounded exponent
zbMATH Keywords: group algebra
Wikidata QID: Q115364437
reviewed by: D. S. Passman
MaRDI profile type: Publication
cites work: On the Lie ideals of a ring
cites work: On rings whose associated Lie rings are nilpotent
cites work: On Lie nilpotent group rings
cites work: Lie Solvable Group Rings
cites work: Observations on group rings
cites work: Q3333199
cites work: Lie Solvable Rings
full work available at URL: 0022-4049(90)90056-n
OpenAlex ID: W2078168966
description: scientific article; zbMATH DE number 4129005