Dependence of Hilbert coefficients

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 $e_{d-t+1}(I,M),..., e_d(I,M)$ 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 $d$.