A finite extension 
of the field 
of rational functions
in the indeterminate 
,
i.e., 
is a root of a polynomial 
,
where 
.
Function fields are sometimes called algebraic function fields.
Function Field
See also
Local Field, Number Field, Riemann SurfaceExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Function Field." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/FunctionField.html