Relative Cohen-Macaulay filtered modules with a view toward relative Cohen-Macaulay modules

Abstract

Let R be a commutative Noetherian ring, a a proper ideal of R and M a finite R-module. It is shown that, if (R, m) is a complete local ring, then under certain conditions a contains a regular element on D R (H c a (M )), where c = cd(a, M ). A non-zerodivisor characterization of relative Cohen-Macaulay modules w.r.t a is given. We introduce the concept of relative Cohen-Macaulay filtered modules w.r.t a and study some basic properties of such modules. In paticular, we provide a non-zerodivisor characterization of relative Cohen-Macaulay filtered modules w.r.t a. Furthermore, a characterization of cohomological dimension filtration of M by the associated prime ideals of its factors is established. As a consequence, we present a cohomological dimension filtration for those modules whose zero submodule has a primary decomposition. Finally, we bring some new results about relative Cohen-Macaulay modules w.r.t a.