 Given a Riemann surface "M", the set of all meromorphic functions defined on "M" is a field, denoted by formula_28 It is a transcendental extension field of formula_6 if we identify every complex number with the corresponding constant function defined on "M".More generally, given an algebraic variety "V" over some field "K", then the function field of "V", consisting of the rational functions defined on "V" and denoted by "K"("V"), is an extension field of "K".An element "x" of a field extension is algebraic over "K" if it is a root of a nonzero polynomial with coefficients in "K".