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The Almost Nilpotent Radical for Near Rings

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Near-Rings and Near-Fields

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Abstract

In this paper we introduce the concept of an almost nilpotent near-ring. We also define the almost nilpotent radical. The concept of a special radical for near-rings has been treated in several non-equivalent, but related ways in the recent literature. We use the version due to K. Kaarli as basis to define the concept of a weakly special radical in near-rings. We show that the almost nilpotent radical is weakly special on the class A of all near-rings which satisfy an extended version of the Andrunakievich Lemma. A includes all d.g. near-rings — and much more. We also give another characterization of the upper nil radical.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Uinversity of Port Elizabeth, P.O. Box 1600, Port Elizabeth, South Africa

    N. J. Groenewald

Authors
  1. N. J. Groenewald
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Editor information

Editors and Affiliations

  1. Department of Mathematics, National Cheng Kung University, Tainan, Taiwan, Republic of China

    Yuen Fong

  2. Department of Mathematics, Texas A & M University, College Station, Texas, USA

    Carl Maxson

  3. Department of Mathematics, University of Edinburgh, Edinburgh, Scotland

    John Meldrum

  4. Institute for Mathematics, Johannes Kepler Universität Linz, Linz, Austria

    Günter Pilz

  5. Department of Mathematics, University of Stellenbosch, Stellenbosch, South Africa

    Andries van der Walt  & Leon van Wyk  & 

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© 2001 Springer Science+Business Media Dordrecht

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Groenewald, N.J. (2001). The Almost Nilpotent Radical for Near Rings. In: Fong, Y., Maxson, C., Meldrum, J., Pilz, G., van der Walt, A., van Wyk, L. (eds) Near-Rings and Near-Fields. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0954-6_9

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  • DOI: https://doi.org/10.1007/978-94-010-0954-6_9

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-3802-7

  • Online ISBN: 978-94-010-0954-6

  • eBook Packages: Springer Book Archive

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