On addition and multiplication of points in a certain class of projective Klingenberg planes Proceedings of the International Congress in Honour of Professor Hari M. Srivastava

Abstract

Let [InlineEquation not available: see fulltext.] be the coordination quadruple of the projective Klingenberg plane (PK-plane) coordinated with dual quaternion ring [InlineEquation not available: see fulltext.], where Q is any quaternion ring over a field. In this paper, we define addition and multiplication of points on the line [InlineEquation not available: see fulltext.] 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. MSC: 51C05, 51N35, 14A22, 16L30. © 2013 Çelik and Erdoǧan; licensee Springer.