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.

کلیدواژه ها:

Associated primes ، cd-filtration ، Cohomological dimension ، system of ideals