Hjelmslev planes over nearrings Original Research Article

In this paper the notion of an H-nearring and an AH-nearring is defined as specialisations of a PK-nearring, which was introduced by Kolb (forthcoming). With the help of H- and AH-nearrings analytical models of projective and affine Hjelmslev planes are constructed. In the distributive case the notion of an H- or AH-nearring and an H- or AH-ring coincide. Finally, some propositions about the endomorphism semigroup of an AK-plane over a PK-nearring are presented.