Affine Klingenbergsche Strukturen

In this paper we define the affine Klingenberg structures (AK-structures) as a generalization of the affine Klingenberg planes (AK-planes) 2]. By means of moduls over the local rings (which need not be free as with the coordinate AK-planes is the case) there is constructed a class of the coordinate AK-structures. In II and III we define the Desarguesian AK-structures. Any coordinate AK-structure is a Desarguesian AK-structure. With the methods established by E.Artin and applied by W.Klingenberg in 4] we show that any Desarguesian AK-structure is isomorphic with the coordinate AK-structure. Some of the results obtained have been applied to the theory of the AK-planes. Thus, for example, it has been shown that it is possible to assume less with the definition of the Desarguesian AK-planes than with 4] or even with 5].