Abstract

An affine Hjelmslev plane is a near affine Hjelmslev plane with a parallelism. It is proved that every strongly n-uniform near affine Hjelmslev plane possesses an even parallelism and, if n > 2, uneven parallelisms as well. Secondly, we prove that a strongly n-uniform affine Hjelmslev plane A has an extension to a strongly n-uniform projective Hjelmslev plane if and only if the parallelism of A is even. The above results are applied to yield the first known examples of affine Hjelmslev planes which possess no extensions to projective Hjelmslev planes.

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