Hostname: page-component-7bb8b95d7b-fmk2r Total loading time: 0 Render date: 2024-09-26T12:36:38.587Z Has data issue: false hasContentIssue false
  • English
  • Français

Complementation in the group of units of matrix rings

Published online by Cambridge University Press:  17 April 2009

Stewart Wilcox
Stewart Wilcox
Affiliation:
20 Macfarlane Street, Davidson, NSW 2085, Australia
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 with 1 and (R) its Jacobson radical. Then 1 + (R) is a normal subgroup of the group of units, G(R). The existence of a complement to this subgroup was explored in a paper by Coleman and Easdown; in particular the ring R = Matn(ℤpk) was considered. We prove the remaining cases to determine for which n, P and k a complement exists in this ring.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 70 , Issue 2 , October 2004 , pp. 223 - 227
Copyright
Copyright © Australian Mathematical Society 2004

References

[1]Bosma, W., Cannon, J. and Playoust, C., ‘The Magma algebra system (I). The user language’, J. Symbolic Computing 24 (1997), 235–265.CrossRefGoogle Scholar
[2]Coleman, C. and Easdown, D., ‘Complementation in the group of units of a ring’, Bull. Austral. Math. Soc. 62 (2000), 183–192.CrossRefGoogle Scholar
[3]Macdonald, I.D., The theory of groups (Krieger Publishing Co. Inc., Malabar, FL, 1988).Google Scholar
[4]Szász, F.A., Radicals of rings (John Wiley & Sons Ltd., Chichester, 1981).Google Scholar