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 also be at least $d-1$ we show $e_{i}(q) \leq 0$ for $i=1, \ldots, d$.
Citation
Lori Mccune. "Hilbert coefficients of parameter ideals." J. Commut. Algebra 5 (3) 399 - 412, FALL 2013. https://doi.org/10.1216/JCA-2013-5-3-399
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