Hilbert coefficients and Buchsbaumness of associated graded rings

Let A be a Noetherian local ring with the maximal ideal and Ian -primary ideal. The purpose of this paper is to generalize Northcottʹs inequality on Hilbert coefficients of I given in Northcott (J. London Math. Soc. 35 (1960) 209), without assuming that A is a Cohen–Macaulay ring. We will investigate when our inequality turns into an equality. It is related to the Buchsbaumness of the associated graded ring of I.