Locally unmixed modules and linearly equivalent topologies

Abstract

Let $R$ be a commutative Noetherian ring, and let $N$ be a non-zero finitely generated $R$-module. The purpose of this paper is to show that $N$ is locally unmixed if and only if, for any $N$-proper ideal $I$ of $R$ generated by $\Ht_N I$ elements, the topology defined by $(IN)^{(n)}$, $n \geq 0$, is linearly equivalent to the $I$-adic topology.