Polarities in n-uniform projective Hjelmslev planes (Q1109333)

The definition of an n-uniform projective Hjelmslev plane given in this paper is equivalent with Drake's definition [\textit{D. A. Drake}, J. Comb. Theory 9, 267-288 (1970; Zbl 0204.210)] by \textit{G. Törner} [Mitt. Math. Sem. Giessen 107, 77 S. (1974; Zbl 0287.05022)]. A polarity of an n-uniform projective Hjelmslev plane (P,B,I) is defined as a one-to-one mapping from point-set onto the line-set and from the line-set onto the point-set such that incidence and neighbor relation are preserved. In Geom. Dedicata 24, 51-76 (1987; Zbl 0628.51007) the author has studied polarities in finite 2-uniform projective Hjelmslev planes. The present paper extends the author's results for finite n-uniform projective Hjelmslev planes with \(n\geq 2\). Here, a general formula for the number of absolute points is obtained, polarities in the Pappian n- uniform projective Hjelmslev planes are studied and configurations formed by the absolute points are investigated.