On the dual of Hilbert coefficients and width of the Associated graded modules over Artinian modules

Abstract

Let $(A,\fm)$ be a commutative quasi-local ring with non-zero identity and let $M$ be an Artinian co-Cohen-Macaulay $R$-module with $\dim M=d$. Let $I\subseteq\fm$ be an ideal of $R$ with $\ell(0:_MI)<\infty$.
In this paper, for $0\leq i\leq d$, we study the dual of Hilbert coefficients $\acute{e}_i(I,M)$ of $I$ relative to $M$. Also, we prove the dual of Huckaba-Marley's inequality. Moreover, we obtain some consequences of this result.