Rationality of some genus 0 extensions of

Authors:
James K. Deveney and Joe Yanik

Journal:
Proc. Amer. Math. Soc. **109** (1990), 53-58

MSC:
Primary 12F20

DOI:
https://doi.org/10.1090/S0002-9939-1990-1007494-5

MathSciNet review:
1007494

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Abstract: Let be a quadratic extension of a field with Galois group . Let be algebraically independent over and let be extended to an automorphism of so that and the extension has order 2. Then is a genus 0 extension of . This paper examines when will be pure transcendental over . It is shown that some important examples from field theory can be realized by this construction. The main result shows that is pure transcendental over if . An example illustrates that it is essential that the second degree polynomial be monic.

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DOI:
https://doi.org/10.1090/S0002-9939-1990-1007494-5

Article copyright:
© Copyright 1990
American Mathematical Society