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Localization of tight closure in two-dimensional rings

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Abstract

It is shown that tight closure commutes with localization in any two-dimensional ringR of prime characteristic if eitherR is a Nagata ring orR possesses a weak test element. Moreover, it is proved that tight closure commutes with localization at height one prime ideals in any ring of prime characteristic.

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Authors and Affiliations

  1. Department of Mathematics, Az-Zahra University, Vanak, Post Code 19834, Tehran, Iran

    Kamran Divaani-Aazar

  2. Institute for Studies in Theoretical Physics and Mathematics, P. O. Box 19395-5746, Tehran, Iran

    Kamran Divaani-Aazar & Massoud Tousi

  3. Department of Mathematics, Shahid Beheshti University, Tehran, Iran

    Massoud Tousi

Authors
  1. Kamran Divaani-Aazar
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  2. Massoud Tousi
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Correspondence to Kamran Divaani-Aazar.

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Divaani-Aazar, K., Tousi, M. Localization of tight closure in two-dimensional rings. Proc. Indian Acad. Sci. (Math. Sci.) 115, 51–56 (2005). https://doi.org/10.1007/BF02829838

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  • DOI: https://doi.org/10.1007/BF02829838

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