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A radical for near-rings

Published online by Cambridge University Press:  14 November 2011

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

Throughout this paper the near-ring N is assumed to be zero symmetric and to satisfy the right distributive law. That is, x · 0 = 0 and (x + y)z = xz + yz for all x, y, z ∈ N. In what follows we generalise the notion of s-primitivity first introduced in an earlier paper by the author (1968), where only distributively generated (d.g.) near-rings with identity were considered. We define a Jacobson type radical Js (N) and show that J1(N)⊇Js(N) ⊇ Q(N), where Q(N) is the intersection of all 0-modular left ideals of N (Pilz). In addition we settle some of the problems remaining from Hartney (1968).

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 93 , Issue 1-2 , 1982 , pp. 105 - 110
Copyright
Copyright © Royal Society of Edinburgh 1982

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