Let $(R,underline{m})$ be a commutative Noetherian local ring and $M$ be a non-zero finitely generated $R$-module. We show that if $R$ is almost Cohen-Macaulay and $M$ is perfect with finite projective dimension, then $M$ is an almost Cohen-Macaulay module. Also, we give some necessary and sufficient condition on $M$ to be an almost Cohen-Macaulay module, by using $Ext$ functors.

an isomorphism? These questions have interest partly because if S and .S’(J, S) are Cohen-Macaulay, then so is gr, S := S/J@ J/J’... [ 16 1 and under these hypotheses if N is perfect and R @ .S(J, S) = .$(I, R), then R and .7(1. R) are Cohen-Macaulay too. Thus, gr,R is Cohen-Macaulay, and its torsion freeness and normality, for exmple, can be characterized in terms of analytic spreads, as in [ ...

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 $lambda(frac{widetilde{i^nm}}{jwidetilde{i^{n-1}m}})$ does not depend on $j$ for all $ngeq 1$, where $j$ is a minimal ...