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

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