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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Ruled function fields


Author: James K. Deveney
Journal: Proc. Amer. Math. Soc. 86 (1982), 213-215
MSC: Primary 12F20
MathSciNet review: 667276
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Abstract: Let $ L = {L_1}({x_1}) = {L_2}({x_2}) \supset K$ where $ {x_i}$ is transcendental over $ {L_i}$, and $ {L_i}$ is a finitely generated transcendence degree 1 extension of $ K$, $ i = 1,2$. If the genus of $ {L_1}/K = 0$, then $ {L_1}$ and $ {L_2}$ are $ K$-isomorphic. If the genus of $ {L_1}/K > 0$, then $ {L_1} = {L_2}$ and moreover $ {L_1}$ is invariant under all automorphisms of $ L/K$. A criterion is also established for a subfield of a ruled field $ L$ to be ruled.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1982-0667276-6
PII: S 0002-9939(1982)0667276-6
Keywords: Ruled field, genus
Article copyright: © Copyright 1982 American Mathematical Society