Let $R$ be a Cohen-Macaulay ring of dimension $n$. Let $M$ be a finitely generated Artinian $R$-module. One can choose an $R$-sequence $(x_1,...,x_n)$ such that there exists a short exact sequence $0\longrightarrow M\longrightarrow (R/(x_1,...,x_n))^k\longrightarrow N\longrightarrow0.$
My approach was using induction on $l(M)$. I wonder if one can prove this by Matlis duality or other methods.