Journal of Commutative Algebra

On Hilbert coefficients of parameter ideals and Cohen-Macaulayness

Kumari Saloni

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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 $g_0(Q)$ and $g_1(Q)$, 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 Vasconcelos {vanishing-conjecture} in unmixed local rings.

Article information

J. Commut. Algebra, Volume 10, Number 3 (2018), 393-410.

First available in Project Euclid: 9 November 2018

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Zentralblatt MATH identifier

Primary: 13D40: Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series 13H10: Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) [See also 14M05]

Hilbert-Samuel Polynomial Hilbert coefficients Cohen-Macaulay ring superficial element


Saloni, Kumari. On Hilbert coefficients of parameter ideals and Cohen-Macaulayness. J. Commut. Algebra 10 (2018), no. 3, 393--410. doi:10.1216/JCA-2018-10-3-393.

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