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Conditions on near-rings which imply that nil N-subgroups are nilpotent

Published online by Cambridge University Press:  20 January 2009

A. Oswald
A. Oswald
Affiliation:
Teesside Polytechnic, Middlesbrough, Cleveland, U.K.
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We assume the reader to be familiar with the basic definitions of near-rings, N-subgroups etc. as presented, for example, in (4). Throughout, N will denote a left near-ring (i.e. a, b, c ∈ N imply a(b + c) = ab + ac) in which 0n = 0 for each n ∈ N. We say that N is strictly semiprime if A2 implies A = (0) where A is an N-subgroup of N. An N-subgroup A is nilpotent if An for some positive integer n and an element a ∈ N is nil if an = 0 for some n. An element a ∈ N is regular if ax = 0 or xa = 0 implies x = 0.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 20 , Issue 4 , September 1977 , pp. 301 - 305
Copyright
Copyright © Edinburgh Mathematical Society 1977

References

REFERENCES

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