Resumen de Equimultiple coefficient ideals
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 k∈{1,…,s}. The largest ideal L containing I such that ei(Ip)=ei(Lp) for each i∈{1,…,k} and each minimal prime p of I is called the k-th equimultiple coefficient ideal denoted by Ik. It is a generalization of the coefficient ideals introduced by Shah for the case of m-primary ideals. We also see applications of these ideals. For instance, we show that the associated graded ring GI(R) satisfies the S1 condition if and only if In=(In)1 for all n.
