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Letbe 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  andare 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 .

Coefficient modules and Ratliff-Rush closures *