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On projective Hjelmslev planes of level n. (English) Zbl 0678.51009

A new definition of projective Hjelmslev planes of level n is given and shown to be equivalent to that of B. Artmann [Math. Z. 112, 163-180 (1969; Zbl 0183.251) and Atti Convegno Geom. Combinat. Appl., Perugia 1970, 27-41 (1971; Zbl 0231.50012)]. This shows that the nth floor of a triangle building is a projective Hjelmslev plane of level n. Thus a link is being established between two different subjects: affine buildings and projective Hjelmslev planes. Sequences introduced by B. Artmann (loc. cit.) are now characterized by means of their inverse limits, and new ones can be constructed. All results hold in the finite as well in the infinite case.
Reviewer: R.Artzy

MSC:

51B99 Nonlinear incidence geometry
51E25 Other finite nonlinear geometries
Full Text: DOI

References:

[1] DOI: 10.1007/BF00148015 · Zbl 0639.51011 · doi:10.1007/BF00148015
[2] DOI: 10.1007/BF00150935 · Zbl 0648.51016 · doi:10.1007/BF00150935
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[7] DOI: 10.1007/BF01224662 · Zbl 0325.50017 · doi:10.1007/BF01224662
[8] DOI: 10.1007/BFb0075518 · doi:10.1007/BFb0075518
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