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- Title
SOME PROPERTIES OF 6-FIGURES AND CROSS-RATIOS IN SOME MOUFANG–KLINGENBERG PLANES.
- Authors
CELIK, NISA; CIFTCI, SÜLEYMAN; AKPINAR, ATILLA
- Abstract
In this paper, we study on Moufang–Klingenberg planes $\mathbf{M}(\mathcal{A})$ defined over a local alternative ring $\mathcal{A}$ 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 $\mathcal{A}$ and the existence of the special 6-figure in $\mathbf{M}(\mathcal{A})$. Moreover, we give a construction which provides an algorithm for "squaring" and "cubing" a cross-ratio of points in $\mathbf{M}(\mathcal{A})$.
- Subjects
ALTERNATIVE rings; NONASSOCIATIVE rings; RATIO &; proportion; ALGORITHMS; CIRCLE-squaring
- Publication
Journal of Algebra & Its Applications, 2010, Vol 9, Issue 2, p173
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S0219498810003811