Abstract
In the last chapter we showed that there are, for example, 588 irreducible monic polynomials of degree 4 in ℤ7[x]. Thus it is conceivable that there could be 588 different fields with 74 = 2401 elements. But that is not really the case. For in Exercise E7 of Chapter 10 you showed, for example, that the two different irreducible polynomials of degree 3 in ℤ2[x] gave simple field extensions which are isomorphic to each other, and you showed in Exercises El and E2 of Chapter 11 that the same is true for certain fields with 9 or 16 elements.
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© 1979 Springer-Verlag New York Inc.
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Childs, L. (1979). Finite Fields. In: A Concrete Introduction to Higher Algebra. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-0065-6_42
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DOI: https://doi.org/10.1007/978-1-4684-0065-6_42
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