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Function Fields

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

Abstract

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.

Keywords

Function Field Prime Divisor Irreducible Polynomial Residue Field Finite Extension 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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