Projective Klingenberg planes over nearrings
type: Item
instance of: scholarly article
title: Projective Klingenberg planes over nearrings
zbMATH Open document ID: 0772.51004
DOI: 10.1007/BF01231002
author: Emanuel Kolb
published in: Journal of Geometry
publication date: 1993-05-04T00:00:00Z
review text: A projective Klingenberg plane is an incidence structure with equivalence relation on the set of points resp. of lines such that there is an incidence epimorphism onto a projective plane. It is shown that examples of such planes can be given by a sort of local nearrings which are therefore called PK-nearrings. The connection with the already known coordinatization by local ternary rings is pointed out [\textit{D. Keppens}, Simon Stevin 62, No. 1, 63-90 (1988; Zbl 0652.51004)]. Examples of PK- nearrings are given with the help of formal power series, in which the multiplication is twisted by a coupling.
Mathematics Subject Classification ID: 51A25
Mathematics Subject Classification ID: 16Y30
zbMATH DE Number: 151852
zbMATH Keywords: projective Klingenberg plane
zbMATH Keywords: nearrings
zbMATH Keywords: coordinatization
zbMATH Keywords: formal power series
reviewed by: Herbert Hotje
MaRDI profile type: Publication
cites work: Q3797777
cites work: Q4735707
cites work: Q4172187
cites work: On local near-rings
cites work: Q3671335
cites work: The Banach fixed point theorem for ultrametric spaces
cites work: Q3249822
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description: scientific article; zbMATH DE number 151852