Dependence of Hilbert coefficients

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.