The relationship between mixed multiplicities of arbitrary ideals in local rings and Hilbert-Samuel multiplicities was solved by Viêt in . In this paper, we extend some important results of Viêt 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.
"Mixed Multiplicities of Modules over Noetherian Local Rings." Tokyo J. Math. 29 (2) 325 - 345, December 2006. https://doi.org/10.3836/tjm/1170348171