Rendiconti del Circolo Matematico di Palermo

, Volume 41, Issue 2, pp 221–230

Star operations and theD+M construction

  • David F. Anderson
Article

Abstract

In this paper, we study star operations on integral domains of the formD+M. In particular, we give an example of a star operation which is not comparable to thet-operation.

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References

  1. [1]
    Anderson D.D.,Star operations induced by overrings, Comm. Algebra16 (1988), 2535–2553.MATHCrossRefMathSciNetGoogle Scholar
  2. [2]
    Anderson D.D., Anderson D.F.,Examples of star operations, Comm. Algebra18 (1990), 1621–1643.MATHCrossRefMathSciNetGoogle Scholar
  3. [3]
    Anderson D.F.,A general theory of class groups, Comm. Algebra16 (1988), 805–847.MATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    Anderson D.F., Ryckaert A.,The class group of D+M, J. Pure Appl. Algebra52 (1988), 199–212.MATHCrossRefMathSciNetGoogle Scholar
  5. [5]
    Bastida E., Gilmer R.,Overrings and divisorial ideals of rings of the form D+M, Michigan Math. J.20 (1973), 79–95.MATHCrossRefMathSciNetGoogle Scholar
  6. [6]
    Brewer J., Rutter E.,D+M constructions with general overrings, Michigan Math. J.23 (1976). 33–42.MATHCrossRefMathSciNetGoogle Scholar
  7. [7]
    Costa D., Mott J., Zafrullah M.,The D+X D S[X]construction, J. Algebra53 (1978), 423–439.MATHCrossRefMathSciNetGoogle Scholar
  8. [8]
    Fossum R.,The Divisor Class Group of a Krull Domain Springer-Verlag, New York, 1973.MATHGoogle Scholar
  9. [9]
    Gilmer R.,Multiplicative Ideal Theory, Marcel Dekker, New York 1972.MATHGoogle Scholar
  10. [10]
    Jaffard P.,Les Systemes d’Ideaux, Dunod, Paris 1960.MATHGoogle Scholar
  11. [11]
    Zafrullah M.,The D+X D S [X] construction from GCD-domains, J. Pure Appl. Algebra50 (1988), 93–107.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer 1992

Authors and Affiliations

  • David F. Anderson
    • 1
  1. 1.Mathematics DepartmentThe University of TennesseeKnoxvilleUSA

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