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Israel Journal of Mathematics

, Volume 37, Issue 4, pp 281–302 | Cite as

Half-factorial-domains

  • Abraham Zaks
Article

Abstract

LetR be a commutative domain with 1. We termR an HFD (Half-Factorial-Domain) provided the equality Π i=1 n χi=Π{f=1/m}y f impliesm=n, whenever thex’s and they’s are non-zero, non-unit and irreducible elements ofR. The purpose of this note is to study HFD’s, in particular, Krull domains that are HFD’s, and to provide examples of HFD’s, that contradict a conjecture of Narkiewicz.

Keywords

Prime Ideal Class Group Length Function Finite Order Principal Ideal 
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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References

  1. 1.
    M. Bass,Algebraic K-theory, Benjamin Inc., 1968.Google Scholar
  2. 2.
    L. Carlitz,A characterization of algebraic number field with class number two, Proc. Amer. Math. Soc.11 (1960), 391–392.MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    L. Claborn,Specified relations in the ideal group, Michigan Math. J.15 (1960), 249–255.MathSciNetGoogle Scholar
  4. 4.
    L. Claborn,Every abelian group is a class group, Pacific J. Math.18 (1966), 219–222.MATHMathSciNetGoogle Scholar
  5. 5.
    E. D. Davis,Overrings of commutative rings II, Trans. Amer. Math. Soc.110 (1964), 196–212.MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    R. M. Fossum,The Divisor Class Group of a Krull Domain, Springer-Verlag, 1973.Google Scholar
  7. 7.
    R. Gilmer and J. Ohm,Integral domains with quotient overrings, Math. Ann.153 (1964), 813–818.CrossRefMathSciNetGoogle Scholar
  8. 8.
    O. Goldman,On a special class of Dedekind domains, Topology 3 Suppl.1 (1964), 113–118.CrossRefMathSciNetGoogle Scholar
  9. 9.
    W. Narkiewicz,Some unsolved problems, Bull. Soc. Math. France25 (1971), 159–164.MATHMathSciNetGoogle Scholar
  10. 10.
    B. Wajnryb and A. Zaks,On the flat overrings of an integral domain, Glasgow Math. J.12 (1971), 162–165.MATHMathSciNetCrossRefGoogle Scholar
  11. 11.
    A. Zaks,Half-factorial domains, Bull. Amer. Math. Soc.82 (1976), 721–724.MATHMathSciNetGoogle Scholar
  12. 12.
    A. Zaks,Dedekind k-subalgebras of k(x), Com. Algebra5 (1977), 347–364.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Hebrew University 1980

Authors and Affiliations

  • Abraham Zaks
    • 1
  1. 1.Department of MathematicsTechnion-Israel Institute of TechnologyHaifaIsrael

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