J Austral Math Soc Ser A 50 pp279--296, 1991.

Centralizer Near-Rings Over Free Ring Modules

C. J. Maxson and A. P. J. ven der Walt

Abstract

We treat centralizer near-rings over ring modules in general, with particular emphasis on the case of free modules, Questions like the following are answered. When is the near-ring a nonring? When is the near-ring simple? What are its maximal and minimal left ideals? What is its subgroups structure? What is the radical? The cases where the ring concerned is a PID or a field are treated in some detail.

1980 AMS Subject Classification (1985 Revision): 16A76

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Authors

C. J. Maxson

Department of Mathematics, Texas A & M University, College Station, Texas 77843, U.S.A.

A. P. J. ven der Walt

Department of Mathematics, Stellenbosch University, Stellenbosch, 7600, South Africa.