English

Hilbert Coefficients of Parameter Ideals

Commutative Algebra 2012-02-09 v2

Abstract

We consider the non-positivity of the Hilbert coefficients for a parameter ideal of a commutative Noetherian local ring. In particular, we show that the second Hilbert coefficient of a parameter ideal of depth at least d-1 is always non-positive and give a condition for the coefficient to be zero. With the added condition that the depth of the associated graded ring is also at least d- we show ei(q)0e_{i}(q) \leq 0 for i=1,...,di=1, ..., d.

Keywords

Cite

@article{arxiv.1111.4186,
  title  = {Hilbert Coefficients of Parameter Ideals},
  author = {Lori McCune},
  journal= {arXiv preprint arXiv:1111.4186},
  year   = {2012}
}
R2 v1 2026-06-21T19:37:44.646Z