Projective Dimensions of Ideals of Prufer Domains

  • Barbara L.Osofsky
Conference paper
Part of the International Centre for Mechanical Sciences book series (CISM, volume 287)


A Prüfer domain has all of its finitely generated ideals projective. Countably but not finitely generated ideals must be of projective dimension 1. A standard argument due to Auslander gives an upper bound for the projective dimension of an ideal I. If I is Nk-generated, then I has projective dimension ≆ = k+1. Here we look at how one might get the reverse inequality.


Exact Sequence Intersection Property Standard Argument Projective Module Projective Dimension 


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  1. [1]
    Auslander, M., On the dimension of modules and algebras. III: Global dimension, Hagoya Hath J.,9, 1955, 67.MATHMathSciNetGoogle Scholar
  2. [2]
    Kaplansky, I., Projective modules, Ann. of Hath. ,68, 1958, 372.MATHMathSciNetGoogle Scholar
  3. [3]
    Osofsky, B., Projective dimension of “nice” directed unions, J. Pure and Applied Algebra, 13, 1978, 179.CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Wien 1984

Authors and Affiliations

  • Barbara L.Osofsky
    • 1
  1. 1.Rutgers UniversityUSA

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