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 \(e_{d-t+1}(I,M),..., e_d(I,M)\) are bounded below and above in terms of the first \(d-t+1\) Hilbert coefficients \(e_0(I,M),...,e_{d-t}(I,M)\) and \(d\).