Classifying Finite Fields

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


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.


Finite Field Minimal Polynomial Irreducible Polynomial Ring Homomorphism Monic Polynomial 
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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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