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Periodica Mathematica Hungarica

, Volume 26, Issue 2, pp 111–114 | Cite as

Centralizer near-rings determined by PID-modules, II

  • P. Fuchs
  • C. J. Maxson
  • A. P. J. Van Der Walt
  • K. Kaarli
Article

Abstract

We answer an open problem in radical theory by showing that there exists a zero-symmetric simple near-ringN with identity such thatJ2(N)=N.

Mathematics subject classification numbers, 1991

Primary 16Y30 Secondary 16N20 Key words and phrases Near-ring radical counterexample 

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References

  1. [1]
    P. Fuchs andC. J. Maxson, Centralizer near-rings determined by PID-modules,Archiv der Math. 56 (1991), 140–147.MR 92a: 16052Google Scholar
  2. [2]
    C. J. Maxson, Piecewise endomorphisms of PID-modules,Results in Math., Vol.18 (1990), 125–132.MR 91f:16058Google Scholar
  3. [3]
    C. J. Maxson andA. P. J. Van Der Walt, Centralizer near-rings over free ring modules,Journal Austral. Math. Soc. 50 (1991), 279–296.MR 92a:16054Google Scholar
  4. [4]
    J. D. P. Meldrum,Near-rings and their Links with Groups, Pitman (Research Note Series No. 134), 1985.MR 88a:16068Google Scholar
  5. [5]
    G. F. Pilz,Near-rings 2nd Edition, North Holland, Amsterdam, 1983.MR 85h:16046Google Scholar

Copyright information

© Akadémiai Kiadó 1993

Authors and Affiliations

  • P. Fuchs
    • 1
  • C. J. Maxson
    • 2
  • A. P. J. Van Der Walt
    • 3
  • K. Kaarli
    • 4
  1. 1.Institut für MathematikJohannes Kepler UniversitätLinzAustria
  2. 2.Department of MathematicsTexas A & M UniversityCollege StationUSA
  3. 3.Department of MathematicsUniversity of StellenboschStellenboschSouth Africa
  4. 4.Department of Algebra and GeometryTartu UniversityTartuEstonia

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