Fundamental theorem of geometry without the 1-to-1 assumption
Document Type
Article
Publication Date
1-1-1999
Abstract
It is proved that any mapping of an n-dimensional affine space over a division ring onto itself which maps every line into a line is semiaffine, if n ∈ {2,3, . . .} and ≠ ℤ2. This result seems to be new even for the real affine spaces. Some further generalizations are also given. The paper is self-contained, modulo some basic terms and elementary facts concerning linear spaces and also - if the reader is interested in other than ℝ, ℤp, or ℂ - division rings. ©1999 American Mathematical Society.
Publication Title
Proceedings of the American Mathematical Society
Recommended Citation
Chubarev, A.,
&
Pinelis, I.
(1999).
Fundamental theorem of geometry without the 1-to-1 assumption.
Proceedings of the American Mathematical Society,
127(9), 2735-2744.
http://doi.org/10.1090/s0002-9939-99-05280-6
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/9765
