Ruled function fields

Deveney, James K.

doi:10.1090/S0002-9939-1982-0667276-6

Ruled function fields
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by James K. Deveney PDF

Proc. Amer. Math. Soc. 86 (1982), 213-215 Request permission

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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