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Complementation in the group of units of a ring

Published online by Cambridge University Press:  17 April 2009

Clare Coleman  and
David Easdown
Clare Coleman
Affiliation:
School of Mathematics and Statistics, University of Sydney, New South Wales 2006, Australia e-mail: cec@maths.usyd.edu.aude@maths.usyd.edu.au
David Easdown
Affiliation:
School of Mathematics and Statistics, University of Sydney, New South Wales 2006, Australia e-mail: cec@maths.usyd.edu.aude@maths.usyd.edu.au
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Abstract

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By adding 1 to elements of the nilradical and Jacobson radical of a ring with identity, normal subgroups of the group of units are obtained. In this paper we record observations about complementation of these subgroups in the group of units of a ring, identifying large classes where complementation takes place and some examples where it fails.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 62 , Issue 2 , October 2000 , pp. 183 - 192
Copyright
Copyright © Australian Mathematical Society 2000

References

[1]Coxeter, H.S.M. and Moser, W.O.J., Generators and relations for discrete groups (Springer-Verlag, Berlin, Heidelberg, New York, 1972).CrossRefGoogle Scholar
[2]Hall, M., The theory of groups (Macmillan, New York, 1959).Google Scholar
[3]McDonald, B., Finite rings with identity (Marcel Dekker, Inc., New York, 1974).Google Scholar