Abstract
Let M be a finitely generated module of dimension d and depth t over a Noetherian local ring (A, \({\mathfrak{m}}\)) and I an \({\mathfrak{m}}\)-primary ideal. In the main result it is shown that the last t Hilbert coefficients \({e_{d-t+1}(I,M),\ldots, e_{d}(I,M)}\) are bounded below and above in terms of the first d − t + 1 Hilbert coefficients \({e_{0}(I,M),\ldots,e_{d-t}(I,M)}\) and d.
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15 September 2017
Unfortunately, there was a gap in the proof of Proposition 2.3, and we have to delete it. Keeping the notation in [2], then the proof of Proposition 2.3 only gives the following result.
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Both authors were partially supported by NAFOSTED (Project 101.01-2011.48). The paper was completed during the stay of the second author at the Vietnam Institute for Advanced Study in Mathematics.
An erratum to this article is available at https://doi.org/10.1007/s00229-017-0975-y.
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Dung, L.X., Hoa, L.T. Dependence of Hilbert coefficients. manuscripta math. 149, 235–249 (2016). https://doi.org/10.1007/s00229-015-0762-6
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DOI: https://doi.org/10.1007/s00229-015-0762-6