# Complementation in the Group of Units of a Ring

## Author

**Clare Coleman** and **David Easdown**

## Status

Research Report 99-18

Date: 20 August 1999

## Abstract

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.

## Key phrases

nilradical. Jacobson radical. complementation. group of units of a ring.

## AMS Subject Classification (1991)

Primary: 16U60

Secondary: 16N20, 60N40

## Content

The paper is available in the following forms:
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- 1999-18.dvi.gz (16kB) or
1999-18.dvi (37kB)

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