The equality I2 = qI in sequentially Cohen-Macaulay rings

Let R be a sequentially Cohen-Macaulay local ring and assume that dim R 2 or that dim R = 1 and e(R) > 1. Then the equality I-2 = qI holds true for every good parameter ideal q of R contained in a sufficiently high power of the maximal ideal m, where I = q :(R) m. The structure of the graded rings gr(I) = circle plus(n >= 0) I-n/I-n+1,I- R(I) = circle plus(n >= 0) I-n, and R'(I) = circle plus(n is an element of Z) I-n associated to I is explored n in connection to their sequential Cohen-Macaulayness. Crown Copyright (C) 2012 Published by Elsevier Inc. All rights reserved.