Hostname: page-component-77c89778f8-fv566 Total loading time: 0 Render date: 2024-07-17T01:35:23.456Z Has data issue: false hasContentIssue false
  • English
  • Français

Central Idempotents in Group Rings

Published online by Cambridge University Press:  20 November 2018

R. G. Burns
R. G. Burns*
Affiliation:
McGill University, Montreal, Quebec
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let R be a ring and G a group. The group ring RG consists of all functions f: G → R with finite support. Addition is pointwise and multiplication is defined for f, h ∊ RG and g ∊ G, by

The support group of f is defined to be the subgroup of G generated by the support of f. The element f is idempotent if ff = f

We prove the following result.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 13 , Issue 4 , December 1970 , pp. 527 - 528
Copyright
Copyright © Canadian Mathematical Society 1970

References

1. Černikov, S. N., On the structure of groups with finite classes of conjugate elements, Dokl. Akad. Nauk SSSR 115 (1957), 60-63.Google Scholar
2. Neumann, B. H., Groups with finite classes of conjugate elements, Proc. London Math. Soc. 1 (1951), 178-187.Google Scholar
3. Passman, D. S., Twisted group algebras of discrete groups (to appear).Google Scholar
4. Rider, Daniel, Central idempotents in group algebras, Bull. Amer. Math. Soc. 72 (1966), 1000-1002.Google Scholar
5. Rudin, Walter and Schneider, Hans, Idempotents in group rings, Duke Math. J. 31 (1964), 585-602.Google Scholar