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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Derivations and the integral closure of ideals
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by Reinhold Hübl and Appendix by Irena Swanson PDF
Proc. Amer. Math. Soc. 127 (1999), 3503-3511 Request permission

Abstract:

Let $(R, \mathfrak {m} )$ be a complete local domain containing the rationals. Then there exists an integer $l$ such that for any ideal $I \subseteq R$, if $f \in \mathfrak {m}$, $f \notin I^{n}$, then there exists a derivation $\delta$ of $R$ with $\delta (f) \notin I^{n+l}$.
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Additional Information
  • Reinhold Hübl
  • Affiliation: NWF I - Mathematik, Universität Regensburg, 93040 Regensburg, Germany
  • Email: Reinhold.Huebl@Mathematik.Uni-Regensburg.de
  • Appendix by Irena Swanson
  • Affiliation: Department of Mathematical Sciences, New Mexico State University, Las Cruces, New Mexico 88003
  • Email: iswanson@mnsu.edu
  • Received by editor(s): November 20, 1997
  • Received by editor(s) in revised form: February 24, 1998
  • Published electronically: May 13, 1999
  • Additional Notes: The author was partially supported by a Heisenberg–Stipendium of the DFG
    The author of the appendix was partially supported by the National Science Foundation.
  • Communicated by: Wolmer V. Vasconcelos
  • © Copyright 1999 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 127 (1999), 3503-3511
  • MSC (1991): Primary 13N05, 13J10
  • DOI: https://doi.org/10.1090/S0002-9939-99-04968-0
  • MathSciNet review: 1618698