Constant Field Extensions
In this chapter we investigate a very important class of extensions of function fields, namely, constant field extensions. Let K/F be a function field with constant field F. For every field extension E of F we want to define a function field KE over E and investigate its properties. We shall confine ourselves to the special case where E/F is algebraic, which is substantially easier and which will suffice for most of the applications we have in mind. However, the general case is both interesting and important. Expositions of the general case can be found in Chevalley  and Deuring .
KeywordsZeta Function Finite Field Function Field Prime Divisor Field Extension
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