Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-27T21:36:01.552Z Has data issue: false hasContentIssue false
  • English
  • Français

An approach to the zero-divisor question for group rings

Published online by Cambridge University Press:  26 February 2010

John Clift
John Clift
Affiliation:
Queen Mary College, London E. 1.
Get access

Extract

G. Higman [5] first considered conditions on a group G sufficient to ensure that for any ring R with no zero-divisors the group-ring RG contains no zero-divisors. It has been shown by various authors that if G belongs to one of the classes of locally indicible groups [5], right-ordered groups [6], polycyclic groups [4] or positive one-relator groups [1] then it is enough that G should be torsionfree. The proofs rely heavily on the special properties of the classes of groups involved but it may be conjectured that it is a sufficient condition in general that G should be torsionfree and no counterexamples are known.

Type
Research Article
Information
Mathematika , Volume 26 , Issue 1 , June 1979 , pp. 88 - 93
Copyright
Copyright © University College London 1979

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Baumslag, G.. “Positive one-relator groups”, Trans. American Math. Soc, 156 (1971), 165–183.CrossRefGoogle Scholar
2.Clift, J. W.. “The zero-divisor problem in group rings”, Dissertation (London University, 1975), 138.Google Scholar
3.Cohen, J. M.. “Zero divisors in group rings”, Com. in Algebra, 2(1) (1974), 1–14.CrossRefGoogle Scholar
4.Farkas, D. R. and Snider, R. L.. “Ko and Noetherian group rings”, J. of Algebra 42 (1976), 192–198.CrossRefGoogle Scholar
5.Higman, G.. “The units of group rings”, Proc. London Math. Soc, 46 (1940), 231–248.CrossRefGoogle Scholar
6.La Grange, R. H. and Rhemtulla., A. H. “A remark on the group rings of order preserving permutation groups”, Canadian Math. Bull., 11 (1968), 679–680.CrossRefGoogle Scholar
7.Rudin, W. and Schneider, H.. “Idempotents in group rings”, Duke Math. J., 31 (1964), 585–602.CrossRefGoogle Scholar