In this chapter we make the basic assumption that K is a finitely generated extension of k of transcendence degree one. If x ∈ K is any transcendental element, then K/k(x) will be a finitely generated algebraic extension, i.e., a finite extension. Furthermore, we assume that k is algebraically closed in K, that is, that every element of K algebraic over k already lies in k. In this situation, we say that K is a function field over k, or sometimes that K/k is a function field.
KeywordsFunction Field Prime Divisor Irreducible Polynomial Residue Field Finite Extension
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