Asymptotic behaviour of standard bases

Guillaume Rond

Asymptotic behaviour of standard bases

Commutative Algebra 2013-01-08 v1

Authors: Guillaume Rond

Abstract

We prove here 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 $n$ .

Keywords

standard basis asymptotic behaviour Noether local ring ideal order bounded Grauert-Hironaka power series ring

Cite

@article{arxiv.1301.1154,
  title  = {Asymptotic behaviour of standard bases},
  author = {Guillaume Rond},
  journal= {arXiv preprint arXiv:1301.1154},
  year   = {2013}
}

Comments

Published in Proceedings of the A.M.S

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