manuscripta mathematica

, Volume 93, Issue 1, pp 137–142 | Cite as

The height of ideals and regular sequences

  • Craig Huneke
  • Vijaylaxmi Trivedi


We prove that given a Noetherian ringR and a finitely generatedR-inoduleM, there exists a finite set of prime idealsΛ inR such that the depth of an arbitrary idealI onM is determined by the height ofI modulo each of the primes inΛ. As an application we answer a question raised by the second author and V. Srinivas concerning m-adic approximations of regular sequences in a local ring.


Local Ring Homomorphic Image Noetherian Ring Regular Ring Regular Sequence 
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Copyright information

© Springer-Verlag 1997

Authors and Affiliations

  • Craig Huneke
    • 1
  • Vijaylaxmi Trivedi
    • 2
  1. 1.Department of MathematicsPurdue UniversityWest LafayetteUSA
  2. 2.School of MathematicsTata Institute of Fundamental ResearchBombayIndia

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