One Construction of an Affine Plane Over a Corps

Authors: Orgest ZAKA, Kristaq FILIPI

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 (α,β), where α and β are elements of corps (K,+,*). Whereas straight-line in corps, the conceptualize by equations of the type x*a+y*b=c, where a≠0K or b≠0K the variables and coefficients are elements of that body. 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 the corps as his ring and properties derived from that definition.

Comments: 9 Pages.

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Submission history

[v1] 2016-02-20 04:32:07

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