Unique Factorization

  • Kenneth Ireland
  • Michael Rosen
Part of the Graduate Texts in Mathematics book series (GTM, volume 84)


The notion of prime number is fundamental in number theory. The first part of this chapter is devoted to proving that every integer can be written as a product of primes in an essentially unique way.

After that, we shall prove an analogous theorem in the ring of polynomials over a field.

On a more abstract plane, the general idea of unique factorization is treated for principal ideal domains.

Finally, returning from the abstract to the concrete, the general theory is applied to two special rings that will be important later in the book.


Prime Number Integral Domain Unique Factorization Great Common Divisor Irreducible Polynomial 
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Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • Kenneth Ireland
  • Michael Rosen
    • 1
  1. 1.Department of MathematicsBrown UniversityProvidenceUSA

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