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Strongly prime near-rings

Published online by Cambridge University Press:  20 January 2009

N. J. Groenewald
N. J. Groenewald
Affiliation:
Department of MathematicsUniversity of Port ElizabethPO Box 16006000 Port Elizabeth, South Africa
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Strongly prime rings were introduced by Handelman and Lawrence [5] and in [2] Groenewald and Heyman investigated the upper radical determined by the class of all strongly prime rings. In this paper we extend the concept of strongly prime to near-rings. We show that the class M of distributively generated near-rings is a special class in the sense of Kaarli [6]. We also show that if N is any distributively generated near-ring, then UM(N), UM denotes the upper radical determined by the class M, coincides with the intersection of all the strongly prime ideals of N.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 31 , Issue 3 , October 1988 , pp. 337 - 343
Copyright
Copyright © Edinburgh Mathematical Society 1988

References

REFERENCES

1.Anderson, T., Kaarli, K. and Wiegandt, R., Radicals and subdirect decomposition, preprint.Google Scholar
2.Groenewald, N. J. and Heyman, G. A. P., Certain classes of ideals in group-rings. Communications in Algebra 9 (1981), 137–148.CrossRefGoogle Scholar
3.Groenewald, N. J. and Potgieter, P. C., A note on the Levitzki radical of a near-ring, J. Austral. Math. Soc. (Series A) 36 (1984), 416–420.Google Scholar
4.Groenewald, N. J., The completely prime radical in near-rings, Acta Math. Hungar. (to appear).Google Scholar
5.Handelman, D. and Lawrence, J., Strongly prime rings, Trans. Amer. Math. Soc. 211 (1975), 209–223.CrossRefGoogle Scholar
6.Kaarli, K., Special radicals of near-rings (in Russian), Tartu Riikl. Ül. Toimetised Vih. 610 (1982), 53–68.Google Scholar
7.Oswald, A., Some topics in the structure theory of near-rings (Doctoral Dissertation, University of York, 1973).Google Scholar
8.Parmenter, M. M., Stewart, P. N. and Wiegandt, R., !On the Groenewald-Heyman strongly prime radical, Quaestiones Math. 7 (1984), 22–240.CrossRefGoogle Scholar
9.Pilz, G., Near-Rings (North-Holland Mathematical Studies, 1977).Google Scholar
10.Van Leeuwen, L. C. A. and Wiegandt, R., Semisimple and torsion-free classes, Acta Math. Academica Scientiarum Hungaricae Tomus 38 (1981), 73–81.CrossRefGoogle Scholar
11.Veldsman, S., The elements in the strongly prime radical of a ring, preprint.Google Scholar