Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Asymptotic behaviour of standard bases


Author: Guillaume Rond
Journal: Proc. Amer. Math. Soc. 138 (2010), 1979-1982
MSC (2010): Primary 13H99, 13C99
Published electronically: January 13, 2010
MathSciNet review: 2596032
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 13H99, 13C99

Retrieve articles in all journals with MSC (2010): 13H99, 13C99


Additional Information

Guillaume Rond
Affiliation: Institut de Mathématiques de Luminy, Université Aix-Marseille 2, Campus de Luminy, case 907, 13288 Marseille cedex 9, France
Email: rond@iml.univ-mrs.fr

DOI: http://dx.doi.org/10.1090/S0002-9939-10-10236-6
PII: S 0002-9939(10)10236-6
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
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.