| Abstrakt: |
Let (R , m) be a d-dimensional Noetherian local ring, M be an R-submodule of the free module F = R p . 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, M ⊆ M { d + p − 1 } F ⊆ ⋯ ⊆ M { 1 } F ⊆ M { 0 } F ⊆ M ¯ such that i-the Buchsbaum-Rim coefficients of M and M { k } F are equal for i = 0 , ... , k , between M and its integral closure M ¯ . 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. [ABSTRACT FROM AUTHOR] |
