Bulletin of the
Korean Mathematical Society BKMS

Let $(R,\m)$ be a Noetherian local ring and $M$ a finitely generated $R$-module. For an integer $s>-1$, we say that $M$ is {\it Cohen-Macaulay in dimension $>s$} if every system of parameters of $M$ is an $M$-sequence in dimension $>s$ introduced by Brodmann-Nhan \cite{BN}. In this paper, we give some characterizations for Cohen-Macaulay modules in dimension $>s$ in terms of the Noetherian dimension of the local cohomology modules $H^i_{\mathfrak m}(M)$, the polynomial type of $M$ introduced by Cuong \cite{C} and the multiplicity $e(\underline x; M)$ of $M$ with respect to a system of parameters $\underline x$.

Keywords: Cohen-Macaulay modules in dimension $>s$, $M$-sequence in dimension $>s$, multiplicity, Noetherian dimension, local cohomology modules

MSC numbers: 13D45, 13E05