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A STUDY ON SUBSTRUCTURES OF R-GROUPS

  • Cho, Yong-Uk (Department of Mathematics College of Education Silla University)
  • Received : 2008.10.25
  • Accepted : 2009.05.09
  • Published : 2009.06.30

Abstract

Throughout this paper, we denote that R is a near-ring and G an R-group. We initiate a study of R-substructures of G, monogenic R-groups, faithful R-groups and faithful D.G. representations of near-rings. Next, we investigate some properties of monogenic R-groups, faithful monogenic R-groups and a generalization of annihilator concepts in R-groups.

Keywords

References

  1. F. W. Anderson and K. R. Fuller, Rings and categories of modules, Springer-Verlag, New York, Heidelberg, Berlin, 1974.
  2. G. Betsch, Primitive near-rings, Math. Z., 130 (1973), 351-361. https://doi.org/10.1007/BF01179162
  3. C. G. Lyons and J. D. P. Meldrum, Characterizing series for faithful d.g. near-rings, Proc. Amer. Math. Soc., 72 (1978), 221-227.
  4. S. J. Mahmood and J. D. P. Meldrum, d.g. near-rings on the infinite dihedral groups, Near-rings and Near-fields, Elsevier Science Publishers B. V.(North-Holland) (1987), 151-166.
  5. J. D. P. Meldrum, Upper faithful d.g. near-rings, Proc. Edinburgh Math. Soc., 26 (1983), 361-370. https://doi.org/10.1017/S0013091500004430
  6. J. D. P, Meldrum, Near-rings and their links with groups, Pitman Advanced Publishing Program, Boston, London, Melbourne, 1985.
  7. G. Pilz, Near-rings, North Holland Publishing Company, Amsterdam, New York, Oxford, 1983.