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On projective Hjelmslev planes of level n

Published online by Cambridge University Press:  18 May 2009

G. Hanssens  and
H. van Maldeghem
G. Hanssens
Affiliation:
Seminarie voor Meetkunde en Kombinatoriek, Rljksuniversiteit van Gent, Krijgslaan 281, B-9000 Gent, Belgium
H. van Maldeghem
Affiliation:
Seminarie voor Meetkunde en Kombinatoriek, Rljksuniversiteit van Gent, Krijgslaan 281, B-9000 Gent, Belgium
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In this paper, we establish a new (but equivalent) definition of projective Hjelmslev planes of level n. This shows that the nth floor of a triangle building is a projective Hjelmslev plane of level n (a result already announced in [9], but left unproved). This will allow us to characterize Artmann-sequences by means of their inverse limits and to construct new ones. We also deduce a new existence theorem for level n projective Hjelmslev planes. All results hold in the finite as well as in the infinite case.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 31 , Issue 3 , September 1989 , pp. 257 - 261
Copyright
Copyright © Glasgow Mathematical Journal Trust 1989

References

1.Artmann, B., Hjelmslev-Ebenen mit verfeinerten Nachbarschaftrelationen, Math. Z. 112 (1969), 163–180.CrossRefGoogle Scholar
2.Artmann, B., Existenz und projektive Limiten von Hjelmslev-Ebenen n-ter Stufe, in Atti del Convegno di Geometria Combinatoria e sue Applicazioni, Perugia (1971), 27–41.Google Scholar
3.A Cronheim, Cartesian groups, formal power series and Hjelmslev-planes, Arch. Math. (Basel) 27 (1976), 209–220.CrossRefGoogle Scholar
4.Drake, D. A., Construction of Hjelmslev planes, J. Geom. 10 (1977), 179–193.CrossRefGoogle Scholar
5.Hughes, D. R. and Piper, F. C., Projective planes (Springer-Verlag, 1972).Google Scholar
6.Ronan, M. A., A universal construction of buildings with no rank 3 residue of spherical type, in Rosati, L. A., ed., Buildings and the geometry of diagrams Proceedings Como 1984, Lecture Notes in Mathematics 1181, (Springer-Verlag, 1986), 242–248.Google Scholar
7.Tits, J., Immeubles de type affine, in Rosati, L. A., ed. Buildings and the geometry of diagrams Proceedings Como 1984, Lecture Notes in Mathematics 1181 (Springer-Verlag, 1986), 157–190.Google Scholar
8.Maldeghem, H. Van, Non-classical triangle buildings, Geom. Dedicata 24 (1987), 123–206.CrossRefGoogle Scholar
9.Maldeghem, H. Van, Valuations on PTRs induced by triangle buildings, Geom. Dedicata 26 (1988), 29–84.CrossRefGoogle Scholar