On Hilbert coefficients of parameter ideals and Cohen-Macaulayness

Abstract

Let (R, m) be an unmixed Noetherian local ring, Q a parameter ideal and K an m-primary ideal of R containing Q. We give a necessary and sufficient condition for R to be Cohen-Macaulay in terms of g0(Q) and g1(Q), the Hilbert coefficients of Q with respect to K. As a consequence, we obtain a result of Ghezzi et al. which settles the negativity conjecture of W. V. Vasconcelos [15] in unmixed local rings.