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Classifying Finite Fields

  • Lindsay N. Childs
Part of the Undergraduate Texts in Mathematics book series (UTM)

Abstract

After some preparatory material on homomorphisms, we prove that for each prime power q = p n , there is, up to isomorphism, a unique field with q elements. We also find a formula for the number of irreducible polynomials of degree n in F q [x] for any p and n, and use it to show that almost every polynomial in ℤ[x] is irreducible.

Keywords

Finite Field Minimal Polynomial Irreducible Polynomial Ring Homomorphism Monic Polynomial 
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 Science+Business Media New York 1995

Authors and Affiliations

  • Lindsay N. Childs
    • 1
  1. 1.Department of MathematicsSUNY at AlbanyAlbanyUSA

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