Skip to main content
Log in

On polarities in the k-uniform n-dimensional projective Hjelmslev space PH(n,GF(q)[t]/tk), q odd

  • Published:
Results in Mathematics Aims and scope Submit manuscript

Abstract

The study of polarities in finite projective Hjelmslev spaces started with [5] where the plane 2-uniform case was treated. The results obtained there have been extended in [6] to the plane k-uniform case (k≧2). The present paper deals with polarities in the k-uniform n-dimensional PH-space PH(n,GF(q) [t] /tk)(k≧2, n≧2) with q odd.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Artmann, B., Hjelmslev-Ebenen mit verfeinerten Nachbarschafts-relatixmen, Math. Z. 112 (1969) 163–180.

    Article  MATH  MathSciNet  Google Scholar 

  2. Drake, D.A., On n-uniform Hjelmslev planes, J. Comb. Theory 9 (1970) 267–288

    Article  MATH  MathSciNet  Google Scholar 

  3. Hanssens, G. Keppens, D. en Van Maldeghem, H., On a theorem of Artmann and an application to triangle buildings, preprint.

  4. Hirschfeld, J.W.P., Projective geometries over finite fields, Clarendon Press Oxford (1979).

  5. Keppens, D., Polarities in finite 2-uniform projective Hjelmslev planes, to appear in Geom. Ded.

  6. Keppens, D., Polarities in n-uniform projective Hjelmslev planes, to appear in Geom. Ded.

  7. Keppens, D., Classical Klingenberg generalized quadrangles, preprint.

  8. Klingenberg, W., Projektive und affine Ebenen mit nachbarelementen, Math. Z. 60 (1954) 384–406.

    Article  MATH  MathSciNet  Google Scholar 

  9. Luck, H. Projektive Hjelmslevraume, J. Reine Angew. Math. 243 (1970) 121–158.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Research supported by I.W.O.N.L. grant no. 840037

Rights and permissions

Reprints and permissions

About this article

Cite this article

Keppens, D. On polarities in the k-uniform n-dimensional projective Hjelmslev space PH(n,GF(q)[t]/tk), q odd. Results. Math. 12, 297–324 (1987). https://doi.org/10.1007/BF03322397

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03322397

Keywords

Navigation