ONE CONSTRUCTION OF AN AFFINE PLANE OVER A CORPS - Zaka, Orgest (JOURNAL OF ADVANCES IN MATHEMATICS, 2016)
In this paper, based on several meanings and statements discussed in the literature, we intend constuction a affine plane about a of whatsoever corps (K,+,*). His points conceive as ordered pairs (Î±,Î²), where Î± and Î² are elements of corps (K,+,*). Whereas straight-line in corps, the conceptualize by equations of the type x*a+y*b=c, where aâ‰ 0K or bâ‰ 0K thevariables and coefficients are elements of that corps. To achieve this construction we prove some theorems which show that the incidence structure A=(P, L, I) connected to the corps K satisfies axioms A1, A2, A3 definition of affine plane. In all proofs rely on the sense of thecorps as his ring and properties derived from that definition.