EQUIMULTIPLE COEFFICIENT IDEALS

摘要

Let (R, m) be a quasi-unmixed local ring and I an equimultiple ideal of R of analytic spread s. In this paper, we introduce the equimultiple coefficient ideals. Fix κ∈ {1,....,s}. The largest ideal L containing I such that e_i (I_p) = e_i (L_p) for each i ∈ {1,..., κ} and each minimal prime p of I is called the κ-th equimultiple coefficient ideal denoted by I_k. It is a generalization of the coefficient ideals introduced by Shah for the case of in-primary ideals. We also see applications of these ideals. For instance, we show that the associated graded ring G_I(R) satisfies the S_I condition if and only if I~n = (I~n)_1 for all n.