Applications of Unique Factorization

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

Abstract

The importance of the notion of prime number should be evident from the results of Chapter 1.

In this chapter we shall give several proofs of the fact that there are infinitely many primes in ℤ. We shall also consider the analogous question for the ring k[x].

The theorem of unique prime decomposition is sometimes referred to as the fundamental theorem of arithmetic. We shall begin to demonstrate its usefulness by using it to investigate the properties of some natural number-theoretic functions.

Keywords

Prime Number Finite Field Unique Factorization Riemann Zeta Function Irreducible Polynomial 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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