Beginning with this chapter we turn attention to polynomials with coefficients in a field. In broad outline the theory follows that for integers: we prove the analogue of the Fundamental Theorem of Arithmetic (Chapter 4), study irreducible polynomials (the analogue of primes), and develop the concepts of congruences and congruence classes, and analogues of Fermat's theorem and the Chinese remainder theorem. When the theory for polynomials is combined wih the theory for integers, what comes out in Chapters 23 and 24 is the theory of finite fields.


Commutative Ring Zero Divisor Chinese Remainder Theorem Congruence Class Broad Outline 
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© Springer-Verlag Berlin Heidelberg 2009

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