ON THE DEPTH OF THE ASSOCIATED GRADED RING OF AN M-PRIMARY IDEAL OF A COHEN-MACAULAY LOCAL RING

[摘要] 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 gr(l)(R) we denote the associated graded ring of I and by depth gr(l)(R) we mean depth (gr(l)(R))M, where M is the maximal homogeneous ideal of gr(l)(R). In this paper we individuate some conditions on I that allow us to determine the value of depth gr(l)(R). It is proved that if J subset-or-equal-to I is a minimal reduction of I such that [GRAPHICS] then depth gr(l)(R) = d - 1; let us remark that lambda denotes the length function. (C) 1994 Academic Press, Inc.

[发布日期] 1994-08-01