ISSN:
1420-8997
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract W. Benz showed that if a field K satisfies certain conditions, then every injection K2 → K2 preserving Minkowsky distance 1 is semilinear up to translation. In this paper we consider one of these conditions. We prove that a non-standard Galois field associated with a Cauchy ultra filter over the set of all prime powers satisfies Benz condition but that the field of rationals does not. The last statement is proved by studying the set of rational points of a certain quartic curve, by considering a Weierstrass cubic birationally equivalent to that quartic.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01223041
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