Abstract
An affine Hjelmslev-plane is called desarguesian if and only if the translations form a transitive group and for each pair t1 and t2 of translations, where each trace of t1 is a trace or t2, there exists a trace preserving endomorphism, which maps t1 in t2. The purpose of this paper is to charakterize desarguesian affine Hjelmslev-planes by means of a condition, which corresponds to the theorem of Desargues in ordinary affine planes, including the case, that each line contains only three classes of neighbour points. This case was omitted in [5].
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