Affine Hjelmslev and generalized affine Hjelmslev planes

Abstract

<p>The first chapter provides a discussion of "the" simplest affine Hjelmslev plane with non-trivial neighhour relation. In the second, we consider a geometry constructed over a locI ring and discuss the relationship between the A. H. ring properties and the A. H. plane axioms. In this way we introduce generalized A. H. planes - incidence structures with parallelism satisfying only the axioms induced by the local ring properties. In the remaining chapters, we coordinatize such a structure and give a proof of the Fundamental Theorem.</p>