Abstract
The following version of the fundamental theorem is proved: Let V, W be vector spaces and g: P(V)\E → P(W) a morphism between the associated projective spaces. If the image of g is not contained in a line, then there exists a semilinear map f: V → W which induces g. The difficulty lies in the fact that the homomorphism of division rings associated to the map f can be nonsurjective. As an application, a short proof of Wigner's theorem is also proposed.
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