Abstract
Let A be a Noetherian local ring with the maximal ideal m and I an m -primary ideal. The purpose of this paper is to generalize Northcott's 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.
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