Complementation in the Group of Units of a Ring


Clare Coleman and David Easdown


Research Report 99-18
Date: 20 August 1999


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


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