Mixed Multiplicities of Modules over Noetherian Local Rings

Abstract

The relationship between mixed multiplicities of arbitrary ideals in local rings and Hilbert-Samuel multiplicities was solved by Viet in [8]. In this paper, we extend some important results of Viet in [8, 9, 10, 11] to modules. We build the concept of (FC)-sequences of modules and use this notion to study reductions of ideals with respect to modules, mixed multiplicities of modules and multiplicities of Rees modules.