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2018 On Hilbert coefficients of parameter ideals and Cohen-Macaulayness
Kumari Saloni
J. Commut. Algebra 10(3): 393-410 (2018). DOI: 10.1216/JCA-2018-10-3-393

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 $g_0(Q)$ 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.

Citation

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Kumari Saloni. "On Hilbert coefficients of parameter ideals and Cohen-Macaulayness." J. Commut. Algebra 10 (3) 393 - 410, 2018. https://doi.org/10.1216/JCA-2018-10-3-393

Information

Published: 2018
First available in Project Euclid: 9 November 2018

zbMATH: 06976323
MathSciNet: MR3874660
Digital Object Identifier: 10.1216/JCA-2018-10-3-393

Subjects:
Primary: 13D40 , 13H10

Keywords: Cohen-Macaulay ring , Hilbert coefficients , Hilbert-Samuel Polynomial , superficial element

Rights: Copyright © 2018 Rocky Mountain Mathematics Consortium

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Vol.10 • No. 3 • 2018
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