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A special class of near rings

Published online by Cambridge University Press:  09 April 2009

Steve Ligh
Steve Ligh
Affiliation:
University of Southwestern Lousiana, Lafayette, Lousiana 70501, U. S. A.
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A near ring is a triple (R, +, · ) such that (R, + ) is a group, (R, ·) is a semigroup, and · is left distributive over +; i.e. w(x + z) = wx + wz for each w, x, z in R. A normal subgroup K of a near ring R is an ideal if (i) (m + k)n − mn is in K for all m, n in R and k in K, and (ii) RK ⊆ K. In particular, kernels of near ring homomorphisms are ideals. For various other definitions and elementary facts about near rings, see [5,8]. For each x in a near ring R, let A(x) = {y ∈ R: xy = 0}. A survey on several recent papers on near rings [2,3,6,7,8] shows that the concept of A(x) being an ideal was the main technique. The purpose of this note is to initiate a study of near rings having the property that each A(x) is an ideal.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 18 , Issue 4 , December 1974 , pp. 464 - 467
Copyright
Copyright © Australian Mathematical Society 1974

References

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