Results on Hilbert coefficients of a Cohen-Macaulay module

Let (R,m) be a commutative Noetherian local ring, M a finitely generated R-module of dimension d, and let I be an ideal of definition for M. In this paper, we extend \cite[Corollary 10(4)]{P} and also we show that if M is a Cohen-Macaulay R-module and d=2, then \lambda(\frac{\widetilde{I^nM}}{J\widetilde{I^{n-1}M}}) does not depend on J for all n\geq 1, where J is a minimal reduction of I.

Results on Hilbert coefficients of a Cohen-Macaulay module Keywords:

Cohen-Macaulay rings , Hilbert series , Hilbert function