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Half-Factorial Domains, a Survey

  • Scott T. Chapman
  • Jim Coykendall
Part of the Mathematics and Its Applications book series (MAIA, volume 520)

Abstract

Let D be an integral domain. D is atomic if every nonzero nonunit of D can be written as a product of irreducible elements (or atoms) of D. Let 1 (D) represent the set of irreducible elements of D. Traditionally, an atomic domain D is a unique factorization domain (UFD) if α 1α n = β 1β m for each ai and β jI (D) implies:
  1. 1.

    n =m,

     
  2. 2.

    there exists a permutation б of {1,... ,n} such that α 1 and β б (i) are associates.

     

Keywords

Prime Ideal Class Group Integral Domain Class Number Integral Closure 
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 Dordrecht 2000

Authors and Affiliations

  • Scott T. Chapman
    • 1
  • Jim Coykendall
    • 2
  1. 1.Department of MathematicsTrinity UniversitySan AntonioUSA
  2. 2.Department of MathematicsNorth Dakota State UniversityFargoUSA

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