Equimultiple coefficient modules

Abstract

Abstract. Let (R;m) be a d-dimensional quasi-unmixed Noetherian local ring and B C F := R^r an equimultiple nitely generated R-module of rank r and analytic spread s. Let I_r(B) denote the 0-th fitting ideal of F/B. In this paper, we use Buchsbaum-Rim polynomial of B F to prove the existence of a chain of modules B C B_x   ... C B₁C B between B̄ and its integral closure B, where B_k is the unique largest submodule of F containing B such that e_i(Bp) = e_i((B_k)_p) for 1 ≤ i ≤ k and every minimal prime p of I_r(B). The number e_i(B_p) is the ith Buchsbaum-Rim  coefficient of B_p in F_p. The module B_k is called the kth equimultiple coefficient module of B C F. We obtain B_x = ( B̃)^u, the unmixed part of the Ratliff-Rush module B̃. In fact, we prove that each Bk is an unmixed Ratliff-Rush module.

Key words: Coefficient ideals, integral closure, reduction, multiplicity.