Hanssens, G.; Van Maldeghem, H. On projective Hjelmslev planes of level n. (English) Zbl 0678.51009 Glasg. Math. J. 31, No. 3, 257-261 (1989). 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 Cited in 7 Documents MSC: 51B99 Nonlinear incidence geometry 51E25 Other finite nonlinear geometries Keywords:projective Hjelmslev planes of level n; building Citations:Zbl 0183.251; Zbl 0231.50012 × Cite Format Result Cite Review PDF 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 [3] Tits, Buildings and the geometry of diagrams Proceedings Como 1984 pp 157– (1986) [4] DOI: 10.1007/BF01110216 · Zbl 0183.25101 · doi:10.1007/BF01110216 [5] Hughes, Projective planes (1972) [6] DOI: 10.1007/BF01933070 · Zbl 0356.50025 · doi:10.1007/BF01933070 [7] DOI: 10.1007/BF01224662 · Zbl 0325.50017 · doi:10.1007/BF01224662 [8] DOI: 10.1007/BFb0075518 · doi:10.1007/BFb0075518 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.