Erratum to: Dependence of Hilbert coefficients

Abstract

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.These inequalities could be useful elsewhere. For the local case, we can only prove Note that The online version of the original article can be found under

Bounds for Hilbert Coefficients

“…, e d−t (I) in the case depth(A) = t ≥ 1. These bounds obtained in [2] depend on e 0 (I). In the case I = Q is a parameter ideal and t = d − 1, the problem of the question is to find bounds for e 2 (Q), .…”

“…Goto and Ozeki [7] established uniform bounds for the Hilbert coefficients of parameter ideals in a generalized Cohen-Macaulay ring. Recently, Dung and Hoa [2] gave bounds for e d−t+1 (I), e d−t+2 (I), . .…”