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 R -module M to be the cd-filtration of M, with respect to a system of ideals. [ABSTRACT FROM AUTHOR]