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Nilpotent subsets of near-rings with minimal condition

Published online by Cambridge University Press:  20 January 2009

S. D. Scott
S. D. Scott
Affiliation:
Department of MathematicsUniversity of AucklandAuckland, New Zealand
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Throughout this paper all near-rings will be zero-symmetric and left distributive. A near-ring with minimal condition on right N-subgroups will be called an near-ring. It is well known (see (1), 3.40, p. 90)) that a nil right N-subgroup of an near-ring is nilpotent. However, in a deeper study of near-rings a stronger result than this is sometimes required (2, p. 77).

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 23 , Issue 3 , October 1980 , pp. 297 - 299
Copyright
Copyright © Edinburgh Mathematical Society 1980

References

REFERENCES

(1)Pilz, G., Near-rings (North-Holland publishing Company, Amsterdam, 1977).Google Scholar
(2)Scott, S. D., Near-rings with minimal condition on right N-subgroups (unpublished research report, University of Birmingham, 1973).Google Scholar