On the Depth of the Associated Graded Ring of an m-Primary Ideal of a Cohen-Macaulay Local Ring Original Research Article

Let (R, m) be a Cohen-Macaulay local ring with maximal ideal m and positive dimension d. Let us assume R has infinite residue field and let I be an m-primary ideal of R. By grl(R) we denote the associated graded ring of I and by depth grl(R) we mean depth (grl(R))M, where M is the maximal homogeneous ideal of grl(R). In this paper we individuate some conditions on I that allow us to determine the value of depth grl(R). It is proved that if J subset of or equal to I is a minimal reduction of I such that [formula] then depth grl(R) = d − 1; let us remark that lambda denotes the length function.