On coefficient ideals

Abstract

Let be a Cohen-Macaulay local ring of dimension with infinite residue field and let I be an primary ideal. Let For let be the ith-coefficient ideal of I. Also let denote the Ratliff-Rush closure of A. Let be the associated graded ring of I. We show that if for then for all . In particular if G is generalized Cohen-Macaulay then for all . As a consequence we get that if A is an analytically unramified domain with G generalized Cohen-Macaulay, then the -ification of the Rees algebra A[It] is .