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Essential Nilpotency in Near-Rings

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Near-Rings and Near-Fields

Part of the book series: Mathematics and Its Applications ((MAIA,volume 336))

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Abstract

In this paper we begin the development of a theory of essential nilpotence for near-rings. We show that the prime radical is essentially nilpotent and there exists a unique largest essentially nilpotent ideal EN(R) in any zerosymmetric near-ring R. Basic properties of EN(R) are determined and examples are provided to illustrate and delimit our theory.

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Reference

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Southwestern Louisiana, 70504, Lafayette, LA, USA

    Gary F. Birkenmeier

Authors
  1. Gary F. Birkenmeier
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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, Brock University, St. Catherines, Ontario, Canada

    Howard E. Bell

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

    Wen-Fong Ke

  4. Department of Mathematics and Statistics, University of New Brunswick, Fredericton, New Brunswick, Canada

    Gordon Mason

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

    Günter Pilz

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© 1995 Springer Science+Business Media Dordrecht

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Birkenmeier, G.F. (1995). Essential Nilpotency in Near-Rings. In: Fong, Y., Bell, H.E., Ke, WF., Mason, G., Pilz, G. (eds) Near-Rings and Near-Fields. Mathematics and Its Applications, vol 336. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0359-6_6

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  • DOI: https://doi.org/10.1007/978-94-011-0359-6_6

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-4160-7

  • Online ISBN: 978-94-011-0359-6

  • eBook Packages: Springer Book Archive

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