Hjelmslev planes over nearrings (Q1923490)

Such notions as nearring, \(H\)-nearring, \(AH\)-nearring and associated with its analytical models of planes are very well known. In his own former papers (4 references) the author introduced the notion of \(PK\)-nearring. This paper is devoted to the study of some connections between Hjelmslev and Klingenberg planes and nearrings. The main results of the paper are the constructions of analytical models of a projective Hjelmslev plane, of an affine Klingenberg plane and of an affine Hjelmslev plane over suitable \(PK\)-nearring. Moreover, some fact about the automorphism group of an \(AK\)-plane over \(PK\)-nearrings are given.