Max Deuring

“{{cite book|title=Lectures on the Theory of Algebraic Functions of One Variable|series=Lecture Notes in Mathematics|volume=314|year=1973|publisher=Springer-Verlag|page=1|url=https://books.google.com/books?id=t557CwAAQBAJ&pg=PA1}}”

“Since an algebraic function w(z) is defined implicitly by an equation of the form f(z,w) = 0, where f is a polynomial, it is understandable that the study of such functions should be possible by algebraic methods. Such methods also have the advantage that the theory can be developed in the most general setting, viz. over an arbitrary field, and not only over the field of complex numbers (the classical case).”