On the CD-filtration of modules with respect to a system of ideals

In this paper, we introduce the concept of the cohomological dimension filtration with respect to a system of ideals.In particular, a characterization of cohomological dimension filtration of a module by the associated prime ideals of its factors is established. As a main result, we provide a necessary and sufficient condition for an ascending chain of submodules of an $\mathfrak{R}$ -module $M$ to be the $\mathrm{cd}$-filtration of $M$, with respect to a system of ideals.