On Recent Developments of Planar Nearrings

  • Wen-Fong Ke


Association Scheme Basic Graph Full Automorphism Group Metacyclic Group Circular Planar 
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  1. [1]
    M. Anshel and J. R. Clay. Planar algebraic systems: some geometric interpretations. J. Algebra 10 (1968), 166–173.Google Scholar
  2. [2]
    K. I. Beidar, Y. Fong, and W.-F. Ke. On finite circular planar nearrings. J. Algebra 185 (1996), 688–709.Google Scholar
  3. [3]
    K. I. Beidar, Y. Fong, and W.-F. Ke. Maximal right nearing of quotients and semigroup generalized polynomial identity. Result. Math. 42 (2002), 12–27.Google Scholar
  4. [4]
    K. I. Beidar, W.-F. Ke. On planar nearrings. Preprint.Google Scholar
  5. [5]
    K. I. Beidar, W.-F. Ke, and H. Kiechle. Circularity of finite groups without fixed points. Monatshefte für Mathematik, to appear.Google Scholar
  6. [6]
    K. I. Beidar, W.-F. Ke, and H. Kiechle. Automorphisms of design groups II. Preprint.Google Scholar
  7. [7]
    K. I. Beidar, W.-F. Ke, C.-H. Liu, and W.-R. Wu. Automorphism groups of certain simple 2-(q, 3, λ) designs constructed from finite fields. Finite Fields Appl 9 (2003), 400–412.Google Scholar
  8. [8]
    Ron Brown. Frobenius groups and classical maximal orders Mem. Amer. Math. Soc. 151 (2001), no. 717.Google Scholar
  9. [9]
    J. R. Clay. Circular block designs from planar nearrings. Ann. Discrete Math. 37 (1988), 95–106.Google Scholar
  10. [10]
    J. R. Clay. Nearrings. Geneses and Applications. Oxford University Press. 1992.Google Scholar
  11. [11]
    J. R. Clay. Geometry in fields. Algebra Colloq. 1 (1994), 289–306.Google Scholar
  12. [12]
    J. H. Conway and A. J. Jones, Trigonometric diophantine equations, Acta Arith. 30 (1976), 229–240.Google Scholar
  13. [13]
    G. Ferrero. Stems planari e bib-disegni. Riv. Mat. Univ. Parma (2) 11 (1970), 79–96.Google Scholar
  14. [14]
    C. Cotti Ferrero, Radicali in quasi-anelli planari, Riv. Mat. Univ. Parma 12 (1986), 237–239.Google Scholar
  15. [15]
    C. Ferrero Cotti, S. Manara Pellegrini, On the homomorphic images of planar nearrings, Sistemi binari e loro applicazioni, Taormina, (me), 1978.Google Scholar
  16. [16]
    W.-F. Ke and H. Kiechle. Characterization of some finite Ferrero pairs. Near-rings and near-fields (Fredericton, NB, 1993), 153–160, Math. Appl., 336, Kluwer Acad. Publ., Dordrecht, 1995.Google Scholar
  17. [17]
    W. F. Ke and H. Kiechle. Automorphisms of certain design groups. J. Algebra 167 (1994), 488–500.Google Scholar
  18. [18]
    W. F. Ke and H. Kiechle. On the solutions of the equation xm + ymzm = 1 in a finite field. Proc. Amer. Math. Soc. 123 (1995), 1331–1339.Google Scholar
  19. [19]
    W.-F. Ke and H. Kiechle. Combinatorial properties of ring generated circular planar nearrings. J. Combin. Theory Ser. A 73 (1996), 286–301.Google Scholar
  20. [20]
    W.-F. Ke and H. Kiechle. Overlaps of basic graphs in circular planar nearing. Preprint.Google Scholar
  21. [21]
    H. Kiechle. Points on Fermat Curves over Finite Fields. Contemporary Math. 168 (1994), 181–183.Google Scholar
  22. [22]
    M. C. Modisett. A characterization of the circularity of certain balanced incomplete block designs. Ph. D. dissertation, University of Arizona, 1988.Google Scholar
  23. [23]
    M. Modisett. A characterization of the circularity of balanced incomplete block designs. Utilitas Math. 35 (1989), 83–94.Google Scholar
  24. [24]
    W. R. Scott, Group Theory, Dover, New York, 1987.Google Scholar
  25. [25]
    H.-M. Sun. Segments in a planar nearing. Discrete Math. 240 (2001), 205–217.Google Scholar
  26. [26]
    H.-M. Sun. PBIB designs and association schemes obtained from finite rings. Discrete Math. 252 (2002), 267–277.Google Scholar
  27. [27]
    G. Wendt. A description of all planar nearrings. Preprint.Google Scholar
  28. [28]
    G. Wendt. Planar nearrings and sandwich nearrings. Preprint.Google Scholar
  29. [29]
    G. Wendt, Planarity in nearrings. Preprint.Google Scholar
  30. [30]
    Joseph A. Wolf. Spaces of constant curvature. (Fifth edition). Publish or Perish, Inc., Houston, TX, 1984.Google Scholar

Copyright information

© Springer 2005

Authors and Affiliations

  • Wen-Fong Ke
    • 1
  1. 1.Department of MathematicsNational Cheng Kung UniversityTainanTaiwan

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