Hilbert coefficients of good I-filtrations of modules

Abstract

Let [Formula: see text] be a finitely generated module of dimension [Formula: see text] over a Noetherian local ring [Formula: see text] and [Formula: see text] an [Formula: see text]-primary ideal. Let be a pair of good [Formula: see text]-filtrations [Formula: see text] and [Formula: see text] of [Formula: see text]. We show that the Hilbert coefficients [Formula: see text] are bounded below and above in terms of [Formula: see text], [Formula: see text], and reduction numbers of [Formula: see text] and [Formula: see text], for all [Formula: see text].