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The height of ideals and regular sequences

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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.

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Authors and Affiliations

  1. Department of Mathematics, Purdue University, 47907, West Lafayette, IN, USA

    Craig Huneke

  2. School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, 400 005, Bombay, India

    Vijaylaxmi Trivedi

Authors
  1. Craig Huneke
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  2. Vijaylaxmi Trivedi
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This article was processed by the author using the Springer-Verlag TEX P Jourlg macro package 1991.

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Huneke, C., Trivedi, V. The height of ideals and regular sequences. Manuscripta Math 93, 137–142 (1997). https://doi.org/10.1007/BF02677462

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  • DOI: https://doi.org/10.1007/BF02677462

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