Classifying Finite Fields
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.
KeywordsFinite Field Minimal Polynomial Irreducible Polynomial Ring Homomorphism Monic Polynomial
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