Function Fields

  • David M. Goldschmidt
Part of the Graduate Texts in Mathematics book series (GTM, volume 215)


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.


Function Field Prime Divisor Irreducible Polynomial Residue Field Finite Extension 
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Copyright information

© Springer-Verlag New York, Inc. 2003

Authors and Affiliations

  • David M. Goldschmidt
    • 1
  1. 1.IDA Center for Communications Research—PrincetonPrincetionUSA

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