A NOTE ON PAPPIAN AFINNE PLANES

Abstract

In (Schmidt and SteinitZ,-1996); an affine plane with Jixed basis ~I ,t2,0}is coordinated. Then, a ternary operation T on R which is a set of pointson I which is dependent on the coordinate system 11,/2, t is deJined. Inaddition, two different binary operation denoted by +,. on R using ternaryoperation T. After then, it is showed that (R,+,.) is a division ring. Inthis paper, Jirst of all we examined the relation between (R, T) ternary ringand Desargues postulate in aJine plane. After then, we showed that (R,+,.)is Jield in case affine plane satisfies Pappus Theorem. This results appearedin theJirst author's Msc thesis.

Özet

( Schmidt ve Ralph,-1996 ) da {a, tl , t 2} tabanina bagl, olarak bir ajindiizlem koordinatlanmtsur. Daha sonra 11,12, t koordinat sisitemine bagltolarak I dogrusu uzerindeki noktalartn kumesi R olmak iizere R kiimesiuzerinde bir T ucli! islem tanimlanarak; (R,+,.) run bir bolumlu halkaoldugu gosterilmistir. Bu makalede ilk olarak afin diizlemde (R, T) iicliihalkasi ile Desargues Postulatt arastndaki ilgi incelendi. Daha sonra, ajinduzlemin Pappus Teoremini saglamasi durumunda (R,+,.) nin bir cisimoldugu gosterildi. Bu sonuclar ilk yazarin Master tezinde gorulebilir.