Asymptotic behaviour of standard bases
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- by Guillaume Rond PDF
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Abstract:
We prove that the elements of any standard basis of $I^n$, where $I$ is an ideal of a Noetherian local ring and $n$ is a positive integer, have order bounded by a linear function in $n$. We deduce from this that the elements of any standard basis of $I^n$ in the sense of Grauert-Hironaka, where $I$ is an ideal of the ring of power series, have order bounded by a polynomial function in $n$.References
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Additional Information
- Guillaume Rond
- Affiliation: Institut de Mathématiques de Luminy, Université Aix-Marseille 2, Campus de Luminy, case 907, 13288 Marseille cedex 9, France
- MR Author ID: 759916
- Email: rond@iml.univ-mrs.fr
- Received by editor(s): January 21, 2009
- Received by editor(s) in revised form: October 1, 2009
- Published electronically: January 13, 2010
- Communicated by: Bernd Ulrich
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 138 (2010), 1979-1982
- MSC (2010): Primary 13H99, 13C99
- DOI: https://doi.org/10.1090/S0002-9939-10-10236-6
- MathSciNet review: 2596032