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manuscripta mathematica

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

The height of ideals and regular sequences

  • Craig Huneke
  • Vijaylaxmi Trivedi
Article
  • 62 Downloads

Summary

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.

Keywords

Local Ring Homomorphic Image Noetherian Ring Regular Ring Regular Sequence 
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

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    Matsumura, H.,Commutative ring theory, Cambridge University Press, 1986Google Scholar
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    Srinivas, V. and Trivedi, V.,The invariance of Hilbert functions of quotients under small perturbations. Journal of Algebra186 (1996), 1–19.zbMATHGoogle Scholar

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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