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On the decomposition of the s-radical of a near-ring

Published online by Cambridge University Press:  20 January 2009

J. F. T. Hartney
J. F. T. Hartney
Affiliation:
Department of Mathematics, University of the Witwatersrand, Johannesburg, South Africa, 2050
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Abstract

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This paper concerns a Jacobson-type radical for the near-ring N. This radical, denoted by Js(N) has an external representation on a type-0N-group of a very special kind. Such N-groups are said to be of type-s. The main objective of this paper is to decompose Js(N) as a sum Js(N) = J1/2(N) + A + B for N satisfying the descending chain condition for N-subgroups. In this decomposition J1/2(N) is nilpotent and A is the unique minimal ideal modulo which Js(N) is nilpotent.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 33 , Issue 1 , February 1990 , pp. 11 - 22
Copyright
Copyright © Edinburgh Mathematical Society 1990

References

REFERENCES

1.Hartney, J. F. T., Radicals and antiradicals in near-rings (Ph.D. thesis, University of Nottingham, 1979).Google Scholar
2.Hartney, J. F. T., A radical for near-rings, Proc. Roy. Soc. Edinburgh 93A (1982), 105–110.CrossRefGoogle Scholar
3.Hartney, J. F. T., An antiradical for near-rings, Proc. Roy. Soc. Edinburgh 96A (1984), 185–191.Google Scholar
4.Laxton, R. R., Prime ideals and the ideal radical of a distributively generated near-ring, Math. Z. 83 (1964), 8–17.CrossRefGoogle Scholar
5.Laxton, R. L. and MACHIN, A. W., On the decomposition of near-rings, Abh. Math. Sem. Univ. Hamburg 38 (1972), 221–230.CrossRefGoogle Scholar
6.Meldrum, J. D. P., Near-rings and their Links with Groups (Research Notes Math. 134, Pitman, 1985).Google Scholar
7.Neumann, Hanna, On varieties of groups and their associated near-rings, Math. Z. 65 (1956), 36–69.CrossRefGoogle Scholar
8.Pilz, Gunter, Near-rings (North-Holland Math. Studies 23, 1977).Google Scholar
9.Scott, S. D., Near-rings and Near-ring Modules (Ph.D. thesis, Australian National University, 1970).Google Scholar
10.Scott, S. D., Formation radicals for near-rings, Proc. London Math. Soc., (3) 25 (1972), 441–464.CrossRefGoogle Scholar