solidot新版网站常见问题,请点击这里查看。
消息
本文已被查看21358次
Isomorphic-Dilations of the skew-fields constructed over parallel lines in the Desargues affine plane. (arXiv:1904.01469v1 [math.MG])
来源于:arXiv
This paper considers dilations and translations of lines in the Desargues
affine plane. A dilation of a line transforms each line into a parallel line
whose length is a multiple of the length of the original line. In addition to
the usual Playfair axiom for parallel lines in an affine plane, further
conditions are given for distinct lines to be parallel in the Desargues affine
plane. This paper introduces the dilation of parallel lines in a finite
Desargues affine plane that is a bijection of the lines. Two main results are
given in this paper, namely, each dilation in a finite Desarguesian plane is an
isomorphism between skew fields constructed over isomorphic lines and each
dilation in a finite Desarguesian plane occurs in a Pappian space. 查看全文>>