Coefficient modules and Ratliff-Rush closures*

Abstract

Let be a d-dimensional Noetherian local ring, M be an R-submodule of the free module . In this work, in analogy to the papers of Liu in [16] and of Ratliff and Rush in [20], if we consider R a formally equidimensional ring and the R-module F/M having finite length, we prove the existence of a unique chain of modules, such that i-the Buchsbaum-Rim coefficients of M and are equal for , between M and its integral closure . This modules will be called Coefficient Modules of M. We also give a colon structure description of these coefficient modules, and, in addition, as consequence of this results, we obtain certain properties of the Ratliff-Rush module of M.