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A theorem on compatible N-groups

Published online by Cambridge University Press:  20 January 2009

S. D. Scott  and
C. G. Lyons
S. D. Scott
Affiliation:
Department of MathematicsUniversity of AucklandNew Zealand
C. G. Lyons
Affiliation:
Department of Mathematics and Computer SciencesJames Madison UniversityHarrisonburgVirginiaU.S.A.
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A near-ring N is a set N with binary operations + and · satisfying the conditions (1) (N, +) is a group, (2) (N, ·) is a semigroup, and (3) · satisfies one of the distributive laws over +. (N, +) need not be an abelian group and if the left distributive law holds, i.e. a · (b + c) = a · b + a · c for all a, b, c ∈ N, then N is called a left near-ring. Similarly, the notion of a right near-ring may be defined.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 25 , Issue 1 , February 1982 , pp. 27 - 30
Copyright
Copyright © Edinburgh Mathematical Society 1982

References

REFERENCES

1.Lyons, C. G. and Meldrum, J. D. P., N-series and tame near-rings, Proc. Roy. Soc. Edinburgh, to appear.Google Scholar
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4.Scott, S. D., Near-rings and near-ring modules (Doctoral Dissertation, Australian National University, 1970).Google Scholar