On the Factorisation of Polynomials

  • Antonio Caminha Muniz Neto
Chapter
Part of the Problem Books in Mathematics book series (PBM)

Abstract

The division algorithm for polynomials provides a notion of divisibility in \(\mathbb K[X]\) when \(\mathbb K=\mathbb Q\),\(\mathbb R\) ou \(\mathbb C\), and such a notion enjoys properties analogous to those of the corresponding concept in \(\mathbb Z\). It is then natural to ask whether there exists some notion of primality in \(\mathbb K[X]\), which furnishes some sort of unique factorisation with properties similar to the unique factorisation of integers. Our purpose in this chapter is to give precise answers to these questions, which shall encompass polynomials with coefficients in \(\mathbb Z_p\), for some prime integer p.

References

  1. 8.
    A. Caminha, An Excursion Through Elementary Mathematics I - Real Numbers and Functions (Springer, New York, 2017)Google Scholar
  2. 11.
    J.B. Conway, Functions of One Complex Variable I (Springer, New York, 1978)Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Antonio Caminha Muniz Neto
    • 1
  1. 1.Universidade Federal do CearáFortalezaBrazil

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