# On the Factorisation of Polynomials

Chapter

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## 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

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

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