On Hilbert coefficients of parameter ideals and Cohen-Macaulayness

2016/09/25 by Saloni, Kumari
#Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1609.07746

Abstract

Let (R, \mathfrak m) be an unmixed Noetherian local ring, Q a parameter ideal and K an \mathfrak 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.

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