On the structure of finite elation Laguerre planes

Quasi-orderings are introduced in arbitrary affine planes and ternary rings as a common generalization of half-orderings and semiorderings. Quasi-ordered affine planes are described algebraically by quasi-ordered ternary rings. A lot of proper quasi-orderings are constructed in ternary rings. These algebraic examples show that all Lenz-Barlotti-classes, as far as they are known to be non-empty, are containing affine planes with proper quasi-orderings.Dedicated to Professor Dr. H. Lenz on the occasion of his 75th birthday