Prime decomposition in number rings

  • Daniel A. Marcus
Part of the Universitext book series (UTX)


We have seen that number rings are not always unique factorization domains: Elements may not factor uniquely into irreducibles. (See exercise 29, chapter 1, and exercise 15, chapter 2 for examples of non-unique factorization.) However we will prove that the nonzero ideals in a number ring always factor uniquely into prune ideals. This can “be regarded as a generalization of unique factorization in , where the ideals are just the principal ideals (n) and the prime ideals are the ideals (p), where p is a prime integer.


Prime Ideal Number Field Principal Ideal Free Abelian Group Monic Polynomial 
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Copyright information

© Springer-Verlag, New York Inc. 1977

Authors and Affiliations

  • Daniel A. Marcus
    • 1
  1. 1.Department of MathematicsCalifornia State Polytechnic UniversityPomonaUSA

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