SOME PROPERTIES OF 6-FIGURES AND CROSS-RATIOS IN SOME MOUFANG-KLINGENBERG PLANES


ÇELİK N., Ciftci S., AKPINAR A.

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, vol.9, no.2, pp.173-184, 2010 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 9 Issue: 2
  • Publication Date: 2010
  • Doi Number: 10.1142/s0219498810003811
  • Title of Journal : JOURNAL OF ALGEBRA AND ITS APPLICATIONS
  • Page Numbers: pp.173-184
  • Keywords: Moufang-Klingenberg planes, local alternative ring, cross-ratio, 6-figure, ratio of 6-figure

Abstract

In this paper, we study on Moufang-Klingenberg planes M(A) defined over a local alternative ring A of dual numbers. We get relations between some special 6-figures and its ratios. Also, we construct a relation between the solvability of the special quadric equation in A and the existence of the special 6-figure in M(A). Moreover, we give a construction which provides an algorithm for "squaring" and "cubing" a cross-ratio of points in M(A).