On addition and multiplication of points in a certain class of projective Klingenberg planes

Abstract

Let be the coordination quadruple of the projective Klingenberg plane (PK-plane) coordinated with dual quaternion ring , where Q is any quaternion ring over a field. In this paper, we define addition and multiplication of points on the line geometrically, also we give the algebraic correspondences of them. Finally, we carry over some well-known properties of ordinary addition and multiplication to our definition.