Small perturbations in generalized Cohen-Macaulay local rings

Let (R, m) be a generalized Cohen-Macaulay local ring of dimension d, and f(1),..., f(r) a part of system of parameters of R. In this paper we give explicit numbers Nsuch that the lengths of all lower local cohomology modules and the Hilbert function of R/( f(1),..., f(r)) are preserved when we perturb the sequence f(1),..., f(r) by epsilon(1),..., epsilon(r) is an element of m(N). The second assertion extends a previous result of Srinivas and Trivedi for generalized Cohen-Macaulay rings. (C) 2021 Published by Elsevier Inc.