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Centralizer near-rings over free ring modules

Published online by Cambridge University Press:  09 April 2009

C. J. Maxson  and
A. P. J. Van Der Walt
C. J. Maxson
Affiliation:
Department of Mathematics Texas A & M University College StationTexas 77843, U.S.A.
A. P. J. Van Der Walt
Affiliation:
Department of Mathematics Stellenbosch UniversityStellenbosch, 7600, South Africa
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Abstract

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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 subgroup structure? What is the radical? The cases where the ring concerned is a PID or a field are treated in some detail.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 50 , Issue 2 , April 1991 , pp. 279 - 296
Copyright
Copyright © Australian Mathematical Society 1991

References

[1]Fuchs, P., Ultraproducts of Ω-groups, (Ph.D.-thesis, Linz, 1985).Google Scholar
[2]Maxson, C. J. and Smith, K. C., ‘Simple near-ring centralizers of finite rings’, Proc. Amer. Math. Soc. 75 (1979), 8–12.CrossRefGoogle Scholar
[3]Maxson, C. J. and Smith, K. C., ‘Centralizer near-rings that are endomorphism rings’, Proc. Amer. Math. Soc. 80 (1980), 189–195.CrossRefGoogle Scholar
[4]Meldrum, J. D. P., Near-rings and their links with groups, (Pitman Research Notes Series, No 134, 1985).Google Scholar
[5]Pilz, G., Near-rings, (North-Holland, American Elsevier, Amsterdam, 1983).Google Scholar