A FORMULA FOR REDUCTION NUMBER OF AN IDEAL RELATIVE TO A NOETHERIAN MODULE

Abstract

Let (A, m) be a Noetherian local ring with infinite residue field and E be a finitely generated d dimensional Cohen-Macaulay A-module. Let b be an ideal of A such that htEb = 0 and λ(b, E) = 1. Assume that bp = 0 for all p ∈ Min(E/bE). Let r(b, E) > 0. We show that if Gb(E) is Cohen-Macaulay, then r(b, E) = a(Gb(E)) + 1.