On Hilbert coefficients and sequentially generalized Cohen–Macaulay modules

Abstract

This paper shows that if [Formula: see text] is a homomorphic image of a Cohen–Macaulay local ring, then [Formula: see text]-module [Formula: see text] is sequentially generalized Cohen–Macaulay if and only if the difference between Hilbert coefficients and arithmetic degrees for all distinguished parameter ideals of [Formula: see text] are bounded.